{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T21:40:08Z","timestamp":1685050808257},"reference-count":187,"publisher":"Elsevier","isbn-type":[{"value":"9780444516206","type":"print"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1016\/s1874-5857(09)70009-3","type":"book-chapter","created":{"date-parts":[[2009,7,1]],"date-time":"2009-07-01T08:16:54Z","timestamp":1246436214000},"page":"195-254","source":"Crossref","is-referenced-by-count":7,"title":["Jacques Herbrand: Life, Logic, and Automated Deduction"],"prefix":"10.1016","author":[{"given":"Claus-Peter","family":"Wirth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00f6rg","family":"Siekmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Benzm\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Serge","family":"Autexier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S1874-5857(09)70009-3_rf0365","first-page":"814","article-title":"Nouvelle demonstration du theoreme d'existence en theorie du corps de classes","volume":"193","author":"Herbrand","year":"1931","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0825","first-page":"1274","article-title":"Sur la theorie de la demonstration","volume":"186","author":"Herbrand","year":"1928","journal-title":"Comptes rendus heb-domadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0830","first-page":"303","article-title":"Non-contradiction des axiomes arithmetiques","volume":"188","author":"Herbrand","year":"1929","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0835","first-page":"1076","article-title":"Sur quelques proprietes des propositions vraies et leurs applications","volume":"188","author":"Herbrand","year":"1929","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0840","first-page":"554","article-title":"Sur le probleme fondamental des mathematiques","volume":"189","author":"Herbrand","year":"1929","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0845","unstructured":"Jacques Herbrand. Recherches sur la Theorie de la Demonstration. PhD thesis, Universite de Paris, 1930. Theses presentees a la faculte des Sciences de Paris pour obtenir le grade de docteur es sciences mathematiques - 1re these: Recherches sur la theorie de la demonstration - 2me these: Propositions donnees par la faculte, Les equations de Fredholm - Soutenues le 1930 devant la commission d'examen - President: M. Vessiot, Examinateurs: MM. Denjoy, Frechet - Vu et approuve, Paris, le 20 Juin 1929, Le doyen de la faculte des Sciences, C. Maurain - Vu et permis d'imprimer, Paris, le 20 Juin 1929, Le recteur de l'Academie de Paris, S. Charlety- No. d'ordre2121, SerieA, No.deSerie 1252 - Imprimerie J. Dziewulski, Varsovie - Univ. de Paris. Also in Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizychnych, Nr. 33, Warszawa. Also in [Herbrand, 1968, pp. 35\u2212153]. Annotated English translation Investigations in Proof Theory by Warren Goldfarb (Chapters 1\u22124) and Burton Dreben and Jean van Heijenoort (Chapter 5) with a brief introduction by Goldfarb and extended notes by Goldfarb (Notes A-C, K-M, O), Dreben (NotesF-I), Dreben and Goldfarb (Notes D, J, and N), and Dreben, George Huff, and Theodore Hailperin (Note E) in [Herbrand, 1971, pp. 44\u2212202]. English translation of \u00a7 5 with a different introduction by Heijenoort and some additional extended notes by Dreben also in [Heijenoort, 1971a, pp. 525\u2212581]. (Herbrand's Ph.D. thesis, his cardinal work, dated April14, 1929; submitted at the Univ. of Paris; defended at the Sorbonne June 11, 1930; printed in Warsaw, 1930.)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0850","first-page":"243","article-title":"Les bases de la logique hilbertienne","volume":"37","author":"Herbrand","year":"1930","journal-title":"Revue de Meta-physique et de Morale"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0855","first-page":"1282","article-title":"Nouvelle demonstration et generalisation d'un theoreme de Minkowski","volume":"191","author":"Herbrand","year":"1930","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0860","first-page":"12","article-title":"Sur le probleme fondamental de la logique mathematique","volume":"24","author":"Herbrand","year":"1931","journal-title":"Revue de Metaphysique et de Morale"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0865","first-page":"186","article-title":"Note non signee sur [Herbrand, 1930]","volume":"6","author":"Herbrand","year":"1931","journal-title":"Annales de l'Universite de Paris"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0870","unstructured":"Inconsistent label replaced with [Herbrand, 1931d] or [Herbrand, 1932a]"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0875","unstructured":"Inconsistent label replaced with [Herbrand, 1932a]"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0880","unstructured":"Jacques Herbrand. Notice pour Jacques Hadamard. 1931. In [Herbrand, 1968, pp. 215\u2212219]. With annotations and a brief introduction by Jean van Heijenoort. English translation Note for Jacques Hadamard by Warren Goldfarb in [Herbrand, 1971, pp. 277\u2212281]. (Abstracts for non-experts of Herbrand's mathematical contributions addressed to his presenter to the Academy of Sciences)."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0885","first-page":"594","article-title":"Sur la theorie des corps de nombres de degre infini","volume":"193","author":"Herbrand","year":"1931","journal-title":"Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0890","first-page":"481","article-title":"Sur la theorie des groupes de decomposition, d'inertie et de ramication","volume":"9","author":"Herbrand","year":"1931","journal-title":"J. de Math. Pures et Appliquees (J. Liouville)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0895","first-page":"1","article-title":"Sur la non-contradiction de l'Arithmetique","volume":"166","author":"Herbrand","year":"1932","journal-title":"J. fur die reine und angewandte Mathematik (Crellesches J.)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0900","first-page":"417","article-title":"Sur les classes des corps circulaires","volume":"9","author":"Herbrand","year":"1932","journal-title":"J. de Math. Pures et Appliquees (J. Liouville)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0905","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BF02940630","article-title":"Sur les theoremes du genre principal et des ideaux princi-paux","volume":"9","author":"Herbrand","year":"1932","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ. Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0910","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/BF01455897","article-title":"Theorie arithmetique des corps de nombres de degre infini-II. Extensions algebriques finies de corps infini","volume":"106","author":"Herbrand","year":"1932","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0915","doi-asserted-by":"crossref","first-page":"105","DOI":"10.24033\/asens.817","article-title":"Une propriete du discriminant des corps algebriques","volume":"49","author":"Herbrand","year":"1932","journal-title":"Annales Scientifiques d l'Ecole Normale Superieure"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0920","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1007\/BF01455898","article-title":"Zur Theorie der algebraischen Funktionen","volume":"106","author":"Herbrand","year":"1932","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0925","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/BF01452860","article-title":"Theorie arithmetique des corps de nombres de degre infini-II. Extensions algebriques de degre infini","volume":"108","author":"Herbrand","year":"1933","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0930","unstructured":"Jacques Herbrand. Le Developpement Moderne de la Theorie des Corps Algebriques - Corps de classes et lois de reciprocite. Memorial des Sciences Mathematiques, Fascicule LXXV. Gauthier-Villars, Paris, 1936. Ed. and with an appendix by Claude Chevalley."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0935","series-title":"Ecrits Logiques","author":"Herbrand","year":"1968"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0940","doi-asserted-by":"crossref","unstructured":"Jacques Herbrand. Logical Writings. Harvard Univ. Press, 1971. Ed. by Warren Goldfarb. Translation of [Herbrand, 1968] with additional annotations, brief introductions, and extended notes by Goldfarb, Burton Dreben, and Jean van Heijenoort. (Still the best source on Herbrand's logical writings today).","DOI":"10.1007\/978-94-010-3072-4"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01449946","article-title":"Begr\u00fcndung des, tertium non datur\u2018 mittels der Hilbertschen Theorie der Widerspruchsfreiheit","volume":"93","author":"Ackermann","year":"1925","journal-title":"Mathematische Zeitschrift"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0015","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1007\/BF01448869","article-title":"\u00dcber die Erf\u00fcllbarkeit gewisser Z\u00e4hlausdr\u00fccke","volume":"100","author":"Ackermann","year":"1928","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0020","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF01450016","article-title":"Zur Widerspruchsfreiheit der Zahlentheorie","volume":"117","author":"Ackermann","year":"1940","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0025","series-title":"An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof","author":"Andrews","year":"2002"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0030","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1023\/B:JARS.0000009552.54063.f3","article-title":"Herbrand Award acceptance speech","volume":"31","author":"Andrews","year":"2003","journal-title":"J. Automated Reasoning"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0035","series-title":"theories of quantification, and proof theory","first-page":"71","article-title":"The L\u00f6wenheim-Skolem Theorem","author":"Anellis","year":"1991"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0040","series-title":"Logic and Its History in the Work and Writings of Jean van Heijenoort","author":"Anellis","year":"1992"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0045","series-title":"Sovremennaja logika: problemy teorii, istorii i primenenija v nauke. Materialy IX Obshcherossijskoj nauchnoj konferencii. Sankt-Peterburg","first-page":"410","article-title":"G\u00f6del and the naming of Skolem functions","author":"Anellis","year":"2006"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0050","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF02952512","article-title":"Algebraische Konstruktion reeller K\u00f6rper","volume":"5","author":"Artin","year":"1927","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0055","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/BF02952513","article-title":"\u00dcber die Zerlegung definiter Funktionen in Quadrate","volume":"5","author":"Artin","year":"1927","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ. Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0060","series-title":"Collected Papers","author":"Artin","year":"1965"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0065","doi-asserted-by":"crossref","unstructured":"Serge Autexier. The core calculus. In 20th Int. Conf. on Automated Deduction, Tallinn, 2005, number 3632 in Lecture Notes in Artificial Intelligence, pages 84\u221298. Springer, 2005.","DOI":"10.1007\/11532231_7"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0070","doi-asserted-by":"crossref","unstructured":"Matthias Baaz and Christian G. Fermuller. Non-elementary speedups between different versions of tableaux. In Int. Conf. on Tableaus and Related Methods, TABLEAUX 95, number 918 in Lecture Notes in Artificial Intelligence, pages 217\u2212230. Springer, 1995","DOI":"10.1007\/3-540-59338-1_38"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0075","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/978-3-7091-9394-5_7","article-title":"Methods of functional extension","volume":"1","author":"Baaz","year":"1995","journal-title":"Collegium Logicum \u2014 Annals of the Kurt G\u00f6del"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0080","series-title":"The Birth of Model Theory \u2014 L\u00f6wenheim\u2019s Theorem in the Frame of the Theory of Relatives","author":"Badesa","year":"2004"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0085","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF01457985","article-title":"Beitr\u00e4ge zur Algebra der Logik, insbesondere zum Entscheidungsproblem","volume":"86","author":"Behmann","year":"1922","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0090","series-title":"Logik-Texte - Kommentierte Auswahl zur Geschichte der modernen Logik","year":"1973"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0095","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/BF01459101","article-title":"Zum Entscheidungsproblem der mathematischen Logik","volume":"99","author":"Bernays","year":"1928","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0100","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF02940604","article-title":"Zusatz zu Hilberts Vortrag \u201e Die Grundlagen der Mathematik\u201c","volume":"6","author":"Bernays","year":"1928","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0105","series-title":"L\u2019\u00e9pist\u00e9mologie fran\u00a7aise","year":"2006"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0110","series-title":"From Peirce to Skolem: A Neglected Chapter in the History of Logic","author":"Brady","year":"2000"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0115","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/BF01449963","article-title":"Zur Begr\u00fcndung der intutionistischen Mathematik I","volume":"93","author":"Brouwer","year":"1925","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0120","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/BF01206621","article-title":"Zur Begr\u00fcndung der intutionistischen Mathematik II","volume":"95","author":"Brouwer","year":"1925","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0125","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/BF01209181","article-title":"Zur Begr\u00fcndung der intutionistischen Mathematik III","volume":"96","author":"Brouwer","year":"1926","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0130","series-title":"Gesammelte Abhandlungen mathematischen und philosophischen Inhalts","author":"Cantor","year":"1932"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0135","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1098\/rsbm.1965.0005","article-title":"Jacques Hadamard","volume":"11","author":"Cartwright","year":"1965","journal-title":"Biographical Memoirs of Fellows of the Royal Society"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0140","series-title":"Symbolic logic and mechanical theorem proving","author":"Chang","year":"1973"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0145","first-page":"13","article-title":"Notice biographique sur Herbrand","author":"Chevalley","year":"1931","journal-title":"Annuaire de l\u2019Association amicale de secours des anciens \u00e9l\u00e8ves de l\u2019\u00c9cole Normale Sup\u00e9rieure"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0150","first-page":"97","article-title":"Sur la pens\u00e9e de Jacques Herbrand","volume":"34","author":"Chevalley","year":"1935","journal-title":"L\u2019Enseignement Math\u00e9matique"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0155","author":"Chevalley","year":"1982"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0160","doi-asserted-by":"crossref","first-page":"250","DOI":"10.2307\/2963593","article-title":"Linear reasoning \u2014 a new form of the Herbrand-Gentzen Theorem","volume":"22","author":"Craig","year":"1957","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0165","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2307\/2963594","article-title":"Three uses of the Herbrand-Gentzen Theorem in relating model theory and proof theory","volume":"22","author":"Craig","year":"1957","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0170","doi-asserted-by":"crossref","first-page":"544","DOI":"10.2307\/2025297","article-title":"Review: Jacques Herbrand: Logical writings by Warren Goldfarb","volume":"71","author":"Dalen","year":"1974","journal-title":"The Journal of Philosophy"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0175","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1145\/321033.321034","article-title":"A computing procedure for quantification theory","volume":"7","author":"Davis","year":"1960","journal-title":"J. of the ACM"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0180","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1090\/psapm\/015\/0170497","article-title":"Eliminating the irrelevant from mechanical proofs","volume":"volume 15","author":"Davis","year":"1963","journal-title":"Proceedings of Symposia in Applied Mathematics"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0185","series-title":"The reception of G\u00f6del\u2019s incompleteness theorems","first-page":"84","author":"Dawson Jr","year":"1991"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0190","series-title":"Prelude to recursion theory: the G\u00f6del-Herbrand correspondence","first-page":"1","author":"Dawson Jr","year":"1993"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0195","series-title":"Kreisel\u2019s unwinding of Artin\u2019s proof","first-page":"113","author":"Delzell","year":"1996"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0200","series-title":"Jacques Herbrand et la th\u00e9orie des nombres","first-page":"3","author":"Dieudonn\u00e9","year":"1982"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0205","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BF01237354","article-title":"Claude Chevalley","volume":"4","author":"Dieudonn\u00e9","year":"1999","journal-title":"Transformation Groups"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0210","series-title":"J. Symbolic Logic","first-page":"393","article-title":"A supplement to Herbrand","author":"Dreben","year":"1963"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0215","series-title":"Herbrand-style consistency proofs","first-page":"419","author":"Dreben","year":"1970"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0220","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1090\/S0002-9904-1963-10990-8","article-title":"False lemmas in Herbrand","volume":"69","author":"Dreben","year":"1963","journal-title":"Bull. AMS"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0225","series-title":"Perspectives on the History of Mathematical Logic","year":"1991"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0230","first-page":"61","article-title":"Souvenirs d\u2019un boursier Rockefeller","volume":"4","author":"Dubreil","year":"1983","journal-title":"Cahiers du s\u00e9minaire d\u2019histoire des math\u00e9matiques"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0235","series-title":"Cahiers dus\u00b4eminaire d\u2019histoire des math\u00b4ematiques","first-page":"301","author":"Dubucs","year":"2006"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0240","series-title":"A Mathematical Introduction to Logic","author":"Enderton","year":"1972"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0245","series-title":"Kreisel\u2019s \u201cunwinding\u201d program","first-page":"247","author":"Feferman","year":"1996"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0250","series-title":"Computers and Thought","year":"1963"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0255","series-title":"Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens","author":"Frege","year":"1879"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0260","unstructured":"Gottlob Frege. Die Grundlagen der Arithmetik. Verlag von M. & H. Marcus, Breslau, 1884. Reprinted 1934, as facsimile: Georg Olms Verlag, Hildesheim, 1990"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0265","series-title":"Grundgesetze der Arithmetik-Begriffsschriftlich abgeleitet","author":"Frege","year":"1893"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0270","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/BF01201353","article-title":"Untersuchungen \u00fcber das logische Schlie\u03b2en","volume":"39","author":"Gentzen","year":"1935","journal-title":"Mathematische Zeitschrift"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0275","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/BF01565428","article-title":"Die Widerspruchsfreiheit derreinen Zahlentheorie","volume":"112","author":"Gentzen","year":"1936","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0280","first-page":"3","article-title":"Die gegenw\u00e4rtige Lage in der mathematischen Grundlagen-forschung-Neue Fassung des Widerspruchsfreiheitsbeweises f\u00fcr die reine Zahlentheorie","volume":"4","author":"Gentzen","year":"1938","journal-title":"Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Neue Folge"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0285","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/BF01564760","article-title":"Beweisbarkeit und Unbeweisbarkeit von Anfangsf\u00e4llen der transfiniten Induktion in der reinen Zahlentheorie","volume":"119","author":"Gentzen","year":"1942","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0290","article-title":"The Collected Papers of Gerhard Gentzen","author":"Gentzen","year":"1969"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0295","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1147\/rd.41.0028","article-title":"A proof method for quantification theory: Its justification and realization","volume":"4","author":"Gilmore","year":"1960","journal-title":"IBM Journal Research and Development"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0300","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01696781","article-title":"Die Vollst\u00e4ndigkeit der Axiome des logischen Funktionenkalk\u00fcls","volume":"37","author":"G\u00f6del","year":"1930","journal-title":"Monatshefte f\u00fcr Mathematik und Physik"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0305","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01700692","article-title":"\u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme I","volume":"38","author":"G\u00f6del","year":"1931","journal-title":"Monatshefte f\u00fcr Mathematik und Physik"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0310","series-title":"On Undecidable Propositions of Formal Mathematical Systems","author":"G\u00f6del","year":"1934"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0315","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1073\/pnas.25.4.220","article-title":"Consistency proof for the generalized continuum hypothesis","volume":"25","author":"G\u00f6del","year":"1939","journal-title":"Proc. of the National Academy of Sciences, U.S.A"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0320","article-title":"Collected Works","author":"G\u00f6del","year":"1986"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0325","doi-asserted-by":"crossref","first-page":"678","DOI":"10.2307\/2272853","article-title":"\u03c9 consistency of number theory via Herbrand's theorem","volume":"39","author":"Goldfarb","year":"1974","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0330","first-page":"103","article-title":"Herbrand\u2019s error and G\u00f6del\u2019s correction","volume":"3","author":"Goldfarb","year":"1993","journal-title":"Modern Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0335","series-title":"Les Entretiens de Zurich sur les Fondements et la M\u00e9thode des Sciences Math\u00e9matiques","first-page":"6","year":"1941"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0340","series-title":"The Psychology of Invention in the Mathematical Field","author":"Hadamard","year":"1949"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0345","unstructured":"Helmut Hasse and Jacques Herbrand Sr.. Letters exchanged between Helmut Hasse and Jacques Herbrand Sr.. Available from the Nieders\u00e4chsische Staatsund Universit\u00e4tsbibliothek - Abteilung f\u00fcr Handschriften und seltene Drucke, G\u00f6ttingen, Germany, 1931"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0350","unstructured":"Jean van Heijenoort. On the relation between the falsifiability tree method and the Herbrand method in quantification theory. Unpublished typescript, Nov. 20, 1968, 12pp.; Jean van Heijenoort Papers, 1946\u22121988, Archives of American Mathematics, Center for American History, Univ. of Texas at Austin, Box3.8\/86-33\/1. Copy in Anellis Archives, 1968"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0355","unstructured":"Jean van Heijenoort. From Frege to G\u00f6del: A Source Book in Mathematical Logic, 1879\u22121931. Harvard Univ. Press, 1971. 2nd rev. ed. (1st ed. 1967)."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0360","first-page":"524","article-title":"Reviews of articles by G. E. Mints","volume":"36","author":"Heijenoort","year":"1971","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0365","unstructured":"Jean van Heijenoort. Herbrand. Unpublished typescript, May 18, 1975, 15pp.; Jean van Heijenoort Papers, 1946\u22121988, Archives of American Mathematics, Center for American History, Univ. of Texas at Austin, Box3.8\/86-33\/1. Copy in Anellis Archives, 1975."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0370","doi-asserted-by":"crossref","unstructured":"Jean van Heijenoort. L\u2019\u0153uvre logique de Herbrand et son contexte historique. 1982. In [Stern, 1982, pp. 57\u221285].","DOI":"10.1016\/S0049-237X(08)71877-9"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0375","unstructured":"Jean van Heijenoort. Absolutism and relativism in logic. 1986. In [Heijenoort, 1986b, pp. 75\u221283]."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0380","unstructured":"Jean van Heijenoort. Selected Essays. Bibliopolis, Napoli, copyright 1985. Also published by Librairie Philosophique J. Vrin, Paris, 1986, 1986"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0385","unstructured":"Jean van Heijenoort. Herbrand\u2019s work in logic and its historical context. 1986. In [Heijenoort, 1986b, pp. 99\u2212121]."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0390","unstructured":"Please search for labels on Herbrand in the bibliography preceeding this list of references!"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0395","series-title":"Sitzungsberichte der Preu\u03b2ischen Akademie der Wissenschaften, Berlin, Physikalisch-mathematische Klasse II","first-page":"173","article-title":"Die formalen Regeln der intuitionistischen Logik","author":"Heyting","year":"1930"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0400","series-title":"Sitzungsberichte der Preu\u03b2ischen Akademie der Wissenschaften, Berlin, Physikalisch- mathematische Klasse II","first-page":"158","article-title":"Die formalen Regeln der intuitionistischen Mathematik","author":"Heyting","year":"1930"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0405","series-title":"Intuitionism \u2014 An Introduction","author":"Heyting","year":"1971"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0410","unstructured":"David Hilbert and Wilhelm Ackermann. Grundz\u00fcge der theoretischen Logik. Springer, 1928."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0415","series-title":"Die Grundlagen der Mathematik","author":"Hilbert","year":"1968"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0420","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02940589","article-title":"Neubegr\u00fcndung der Mathematik (Erste Mitteilung)","volume":"1","author":"Hilbert","year":"1922","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ. Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0425","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF01448445","article-title":"\u00dcber das Unendliche","volume":"88","author":"Hilbert","year":"1926","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0430","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF02940602","article-title":"Die Grundlagen der Mathematik - Vortrag, gehalten auf Einladung des Mathematischen Seminars im Juli 1927 in Hamburg","volume":"6","author":"Hilbert","year":"1928","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ. Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0435","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/BF01457953","article-title":"Die Grundlegung der elementaren Zahlenlehre","volume":"104","author":"Hilbert","year":"1931","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0440","doi-asserted-by":"crossref","unstructured":"David Hilbert. Gesammelte Abhandlungen. Springer, 1932ff..","DOI":"10.1007\/978-3-642-50831-8"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0445","doi-asserted-by":"crossref","unstructured":"K. Jaakko J. Hintikka. The Principles of Mathematics Revisited. Cambridge Univ. Press, 1996.","DOI":"10.1017\/CBO9780511624919"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0450","series-title":"Consequences of the Axiom of Choice","author":"Howard","year":"1998"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0455","series-title":"Critik der reinen Vernunft","author":"Kant","year":"1787"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0460","first-page":"150","article-title":"On notation for ordinal numbers","volume":"3","author":"Kleene","year":"1938"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0465","series-title":"Introduction to Metamathematics","author":"Kleene","year":"1952"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0470","first-page":"241","article-title":"On the interpretation of non-finitist proofs \u2014 Part I","volume":"16","author":"Kreisel","year":"1951","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0475","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2307\/2267457","article-title":"On the interpretation of non-finitist proofs \u2014 Part II","volume":"17","author":"Kreisel","year":"1952","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0480","first-page":"155","article-title":"Mathematical significance of consistency proofs","volume":"23","author":"Kreisel","year":"1958"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0485","first-page":"39","article-title":"Finiteness theorems in arithmetic: an application of Herbrand's theorem for \u03a32-formulas","author":"Kreisel","year":"1982"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0490","series-title":"Helmut Hasse-Emmy Noether \u2014 Die Korrespondenz 1925\u22121935","author":"Lemmermeyer","year":"2006"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0495","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/BF01458217","article-title":"\u00dcber M\u00f6glichkeiten im Relativkalk\u00fcl","volume":"76","author":"L\u00f6wenheim","year":"1915","journal-title":"Mathematische Annalen"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0500","series-title":"Automated Theorem Proving: A Logical Basis","author":"Loveland","year":"1978"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0505","series-title":"The Legacy of Mario Pieri in Geometry and Arithmetic","author":"Marchisotto","year":"2007"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0510","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0747-7171(92)90011-R","article-title":"Unification under a mixed prefix","volume":"14","author":"Miller","year":"1992","journal-title":"J. Symbolic Computation"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0515","first-page":"98","article-title":"A house divided against itself: The emergence of first-order logic as the basis for mathematics","author":"Moore","year":"1987"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0520","series-title":"Intuitionism and Proof Theory. Proceedings of the International Conference Intuitionism and Proof Theory, Buffalo, 1968","year":"1970"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0525","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1515\/crll.1925.154.219","article-title":"Eine Axiomatisierung der Mengenlehre","volume":"154","author":"Neumann","year":"1925","journal-title":"J. f\u00fcr die reine und angewandte Mathematik (Crellesches J.)"},{"issue":"128","key":"10.1016\/S1874-5857(09)70009-3_bb0530","article-title":"Berichtigung zu der Arbeit Eine Axiomatisierung der Mengenlehre \u201c","volume":"155","author":"Neumann","year":"1926","journal-title":"J. f\u00fcr die reine und angewandte Mathematik (Crellesches J.)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0535","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01475439","article-title":"Zur Hilbertschen Beweistheorie","volume":"26","author":"Neumann","year":"1927","journal-title":"Mathematische Zeitschrift"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0540","first-page":"669","article-title":"Die Axiomatisierung der Mengenlehre","volume":"27","author":"Neumann","year":"1928"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0545","series-title":"Proc. Western Joint Computer Conf.","first-page":"218","article-title":"Empirical explorations with the Logic Theory Machine: A case study in heuristics","author":"Newell","year":"1957"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0550","first-page":"32","article-title":"A reduction in the number of primitive propositions of logic","volume":"19","author":"Nicod","year":"1917","journal-title":"Proc. Cambridge Philosophical Soc."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0555","series-title":"Research Report MPI-I-96-2010, Max-Planck-Institut f\u00fcr Informatik, Im Stadtwald, D-66123 Saarbr\u00fccken","article-title":"Strong skolemization","author":"Nonnengart","year":"1996"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0560","series-title":"Kreiseliana \u2014 About and Around Georg Kreisel","year":"1996"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0565","first-page":"249","article-title":"Finitism and intuitive knowledge","author":"Parsons","year":"1998"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0570","doi-asserted-by":"crossref","first-page":"180","DOI":"10.2307\/2369451","article-title":"On the algebra of logic: A contribution to the philosophy of notation","volume":"7","author":"Peirce","year":"1885","journal-title":"American J. of Mathematics"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0575","series-title":"A Chronological Edition Vol. 5","article-title":"Writings of Charles S. Peirce","author":"Peirce","year":"1993"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0580","series-title":"Studies in the History of Mathematics","year":"1987"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0585","series-title":"Il Bollettino delle seduta della Accademia Gioenia di Scienze Naturali in Catania, Series2","first-page":"26","article-title":"Sopra gli assiomi aritmetici","author":"Pieri","year":"1907"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0590","first-page":"92","article-title":"\u00dcber die Vollst\u00e4ndigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt","author":"Presburger","year":"1930"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0595","series-title":"Hilbert","author":"Reid","year":"1970"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0600","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF01403065","article-title":"A modular construction of unramified p-extensions of Q(\u00b5p)","volume":"34","author":"Ribet","year":"1976","journal-title":"Inventiones mathematicae"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0605","series-title":"Handbook of Automated Reasoning.","year":"2001"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0610","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1145\/321250.321253","article-title":"A machine-oriented logic based on the resolution principle","volume":"12","author":"Robinson","year":"1965","journal-title":"J. of the ACM"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0615","first-page":"5","article-title":"On the history of Artins L-functions and conductors \u2014 seven letters from Artin to Hasse in the year 1930","volume":"19","author":"Roquette","year":"2000","journal-title":"Mitteilungen der Mathematischen Gesellschaft in Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0620","series-title":"Personal e-mail communications with Peter Roquette","article-title":"The correspondence Helmut Hasse-Jacques Herbrand","author":"Roquette","year":"2007"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0625","unstructured":"Peter Roquette, editor. Helmut Hasse-Jacques Herbrand \u2014 The complete correspondence, including the six letters of Herbrand to Hasse, dated from May 11 to July 23, 1931, and a letter from Joseph H. M. Wedderburn to Hasse on Herbrand\u2019s planned visit to Princeton, dated May 25, 1931. To appear."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0630","doi-asserted-by":"crossref","first-page":"87","DOI":"10.2307\/2269028","article-title":"Extensions of some theorems of G\u00f6del and Church","volume":"1","author":"Rosser","year":"1936","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0635","series-title":"Equivalents of the Axiom of Choice.","author":"Rubin","year":"1985"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0640","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2307\/2271725","article-title":"The consistency of number theory via Herbrand\u2019s Theorem","volume":"38","author":"Scanlon","year":"1973","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0645","series-title":"The Philosophy of Mathematics Today.","year":"1998"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0650","article-title":"Vorlesungen \u00fcber die Algebra der Logik","volume":"Vol. 3","author":"Schr\u00f6der","year":"1895"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0655","series-title":"Beweistheorie","author":"Sch\u00fctte","year":"1960"},{"issue":"2","key":"10.1016\/S1874-5857(09)70009-3_bb0660","doi-asserted-by":"crossref","first-page":"172","DOI":"10.2178\/bsl\/1120231628","article-title":"Only two letters: The correspondence between Herbrand and G\u00f6del","volume":"11","author":"Sieg","year":"2005","journal-title":"The Bulletin of Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0665","series-title":"Automation of Reasoning","year":"1983"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0670","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0747-7171(89)80012-4","article-title":"Unification theory","volume":"7","author":"Siekmann","year":"1989","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0675","first-page":"1","article-title":"Untersuchungen \u00fcber die Axiome des Klassenkalk\u00fcls und \u00fcber Produktations- und Summationsprobleme, welche gewisse Klassen von Aussagen betreffen","volume":"3","author":"Skolem","year":"1919"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0680","first-page":"1","article-title":"Logisch-kombinatorische Untersuchungen \u00fcber die Erf\u00fcllbarkeit und Beweisbarkeit mathematischer S\u00e4tze nebst einem Theorem \u00fcber dichte Mengen","volume":"4","author":"Skolem","year":"1920","journal-title":"Skrifter, Norske Videnskaps-Akademi i Oslo (= Videnskapsselskapet i Kristiania), Matematisk-Natur- videnskapelig Klasse"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0685","first-page":"1","article-title":"Begr\u00fcndung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Ver\u00e4nderlichen mit unendlichem Ausdehnungsbereich","volume":"6","author":"Skolem","year":"1923","journal-title":"Skrifter, Norske Videnskaps-Akademi i Oslo (= Videnskapsselskapet i Kris- tiania), Matematisk-Naturvidenskapelig Klasse"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0690","series-title":"Proc. 5th Scandinaviska Matematikerkongressen, Helsingfors, July 4\u22127, 1922","first-page":"217","article-title":"Einige Bemerkungen zur axiomatischen Begr\u00fcndung der Mengenlehre","author":"Skolem","year":"1923"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0695","first-page":"125","article-title":"\u00dcber die mathematische Logik (Nach einem Vortrag gehalten im Norwegischen Mathematischen Verein am 22. Oktober 1928)","volume":"10","author":"Skolem","year":"1928","journal-title":"Nordisk Matematisk Tidskrift"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0700","first-page":"1","article-title":"\u00dcber einige Grundlagenfragen der Mathematik","volume":"4","author":"Skolem","year":"1929","journal-title":"Skrifter, Norske Videnskaps-Akademi i Oslo (= Videnskapsselskapet i Kristiania), Matematisk-Naturviden- skapelig Klasse"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0705","unstructured":"Thoralf Skolem. Sur la port\u00e9e du th\u00e9or\u00e8me de L\u00f6wenheim-Skolem. 1941. In [Gonseth, 1941, pp. 25\u221252]. Also in [Skolem, 1970, pp. 455\u2212482]."},{"key":"10.1016\/S1874-5857(09)70009-3_bb0710","unstructured":"Thoralf Skolem. Selected Works in Logic. Universitetsforlaget Oslo, 1970. Ed. by Jens E. Fenstad. (Without index, but with most funny spellings in the newly set titles)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0715","series-title":"First-Order Logic","author":"Smullyan","year":"1968"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0720","series-title":"Presburger\u2019s Article on Integer Arithmetic: Remarks and Translation","author":"Stanisfer","year":"1984"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0725","series-title":"Proc. of the Herbrand Symposium, Logic Colloquium\u201981, Marseilles, France, July 1981","year":"1982"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0730","doi-asserted-by":"crossref","first-page":"524","DOI":"10.2307\/2026089","article-title":"Finitism","volume":"78","author":"Tait","year":"1981","journal-title":"J. of Philosophy"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0735","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1093\/philmat\/nkj011","article-title":"G\u00f6del\u2019s correspondence on proof theory and constructive mathematics","volume":"14","author":"Tait","year":"2006","journal-title":"Philosophia Mathematica (III)"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0740","series-title":"A Decision Method for Elementary Algebra and Geometry","author":"Tarski","year":"1951"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0745","first-page":"1","article-title":"The last months of Gerhard Gentzen in Prague","volume":"1","author":"Vihan","year":"1995","journal-title":"Collegium Logicum \u2014 Annals of the Kurt G\u00f6del Society"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0750","series-title":"Automated Proof Search in Non-Classical Logics","author":"Wallen","year":"1990"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0755","first-page":"17","article-title":"A survey of Skolem\u2019s work in logic","author":"Wang","year":"1970"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0760","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF02102305","article-title":"\u00dcber die neue Grundlagenkrise der Mathematik","volume":"14","author":"Weyl","year":"1921","journal-title":"Mathematische Zeitschrift"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0765","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/BF02940603","article-title":"Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag \u00fcber die Grundlagen der Mathematik","volume":"6","author":"Weyl","year":"1928","journal-title":"Abhandlungen aus dem mathematischen Seminar der Univ. Hamburg"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0770","series-title":"Principia Mathematica","author":"Whitehead","year":"1910-1913"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0775","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/jigpal\/12.1.1","article-title":"Descente Infinie + Deduction","volume":"12","author":"Wirth","year":"2004","journal-title":"Logic J. of the IGPL"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0780","series-title":"lim+, \u03b4+, and Non-Permutability of \u03b2-Steps","author":"Wirth","year":"2006"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0785","series-title":"J. Applied Logic","article-title":"Hilbert\u2019s epsilon as an operator of indefinite committed choice","author":"Wirth","year":"2008"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0790","unstructured":"Claus-Peter Wirth. Shallow confluence of conditional term rewriting systems. J. Symbolic Computation. To appear. http:\/\/www.ags.uni-sb.de\/~cp\/p\/shallow"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0795","article-title":"Lectures on the Foundations of Mathematics, Cambridge","author":"Wittgenstein","year":"1989"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0800","series-title":"1st Int. Symposium on G\u00f6del\u2019s Theorem, Paris, May 27\u221229, 1991","year":"1993"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0805","series-title":"Hilbert\u2019s Finitism: Historical, Philosophical, and Metamathematical Perspectives","author":"Zach","year":"2001"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0810","series-title":"M\u00e9morial des Sciences Math\u00e9matiques, Fascicule XV","article-title":"La Logique des Math\u00e9matiques","author":"Zaremba","year":"1926"},{"key":"10.1016\/S1874-5857(09)70009-3_bb0815","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1080\/014453409108837186","article-title":"Moj\u017cesz Presburger: Life and work","volume":"12","author":"Zygmunt","year":"1991","journal-title":"History and Philosophy of Logic"}],"container-title":["Handbook of the History of Logic","Logic from Russell to Church"],"original-title":[],"link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1874585709700093?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1874585709700093?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T21:13:16Z","timestamp":1685049196000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1874585709700093"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9780444516206"],"references-count":187,"URL":"https:\/\/doi.org\/10.1016\/s1874-5857(09)70009-3","relation":{},"ISSN":["1874-5857"],"issn-type":[{"value":"1874-5857","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}