{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T16:00:06Z","timestamp":1721923206895},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2010,7,16]],"date-time":"2010-07-16T00:00:00Z","timestamp":1279238400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1007\/s00153-010-0199-2","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T21:35:51Z","timestamp":1279229751000},"page":"773-798","source":"Crossref","is-referenced-by-count":1,"title":["Consistency statements and iterations of computable functions in I\u03a31 and PRA"],"prefix":"10.1007","volume":"49","author":[{"given":"Joost J.","family":"Joosten","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,7,16]]},"reference":[{"issue":"3","key":"199_CR1","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0168-0072(02)00030-1","volume":"118","author":"J. Avigad","year":"2002","unstructured":"Avigad J.: Saturated models of universal theories. Ann. Pure Appl. Log. 118(3), 219\u2013234 (2002)","journal-title":"Ann. Pure Appl. Log."},{"key":"199_CR2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0168-0072(96)00045-0","volume":"85","author":"L. Beklemishev","year":"1997","unstructured":"Beklemishev L.: Induction rules, reflection principles, and provably recursive functions. Ann. Pure Appl. Log. 85, 193\u2013242 (1997)","journal-title":"Ann. Pure Appl. Log."},{"issue":"6","key":"199_CR3","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s00153-002-0158-7","volume":"42","author":"L. Beklemishev","year":"2003","unstructured":"Beklemishev L.: Proof-theoretic analysis by iterated reflection. Arch. Math. Log. 42(6), 515\u2013552 (2003)","journal-title":"Arch. Math. Log."},{"key":"199_CR4","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0049-237X(98)80017-7","volume-title":"Handbook of Proof Theory","author":"S. Buss","year":"1998","unstructured":"Buss S.: First-order proof theory of arithmetic. In: Buss, S. (eds) Handbook of Proof Theory, pp. 79\u2013148. Elsevier, North-Holland Amsterdam (1998)"},{"key":"199_CR5","unstructured":"Ferreira, F.: Yet another proof of Parsons\u2019 theorem (2002). Not yet published"},{"key":"199_CR6","unstructured":"Gaifman, H., Dimitracopoulos, C.: Fragments of Peano\u2019s arithmetic and the MDRP theorem. In: Logic and algorithmic (Zurich, 1980), (Monograph. Enseign. Math., 30), pp. 187\u2013206. University of Gen\u00e8ve, Gen\u00e8ve (1982)"},{"key":"199_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-22156-3","volume-title":"Metamathematics of First Order Arithmetic","author":"P. H\u00e1jek","year":"1993","unstructured":"H\u00e1jek P., Pudl\u00e1k P.: Metamathematics of First Order Arithmetic. Springer, Berlin, Heidelberg, New York (1993)"},{"key":"199_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-86894-8","volume-title":"Grundlagen der Mathematik, Vols I and II, 2d ed","author":"D. Hilbert","year":"1968","unstructured":"Hilbert D., Bernays P.: Grundlagen der Mathematik, Vols I and II, 2d ed. Springer, Berlin (1968)"},{"key":"199_CR9","unstructured":"Ignjatovic, A.: Fragments of first and Second Order Arithmetic and Length of Proofs. Ph.D. thesis, University of California, Berkeley (1990)"},{"issue":"2","key":"199_CR10","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1305\/ndjfl\/1117755145","volume":"46","author":"J. Joosten","year":"2005","unstructured":"Joosten J.: On interpretability in PRA; the closed fragment of the interpretability logic of PRA with a constant for I\u03a31. Notre Dame J. Formal Log. 46(2), 127\u2013146 (2005)","journal-title":"Notre Dame J. Formal Log."},{"key":"199_CR11","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532132.001.0001","volume-title":"Models of Peano Arithmetic","author":"R. Kaye","year":"1991","unstructured":"Kaye R.: Models of Peano Arithmetic. Oxford University Press, Oxford (1991)"},{"key":"199_CR12","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF01117472","volume":"1","author":"G. Mints","year":"1972","unstructured":"Mints G.: Quantifier-free and one-quantifier systems. J. Soviet Math. 1, 71\u201384 (1972) First published in Russian in 1971","journal-title":"J. Soviet Math."},{"key":"199_CR13","doi-asserted-by":"crossref","first-page":"494","DOI":"10.2307\/2269958","volume":"36","author":"R. Parikh","year":"1971","unstructured":"Parikh R.: Existence and feasibility in arithmetic. J. Symbolic Log. 36, 494\u2013508 (1971)","journal-title":"J. Symbolic Log."},{"key":"199_CR14","first-page":"459","volume-title":"Intuitionism and Proof Theory","author":"C. Parsons","year":"1970","unstructured":"Parsons C.: On a number-theoretic choice schema and its relation to induction. In: Kino, A., Myhill, J., Vessley, R. (eds) Intuitionism and Proof Theory, pp. 459\u2013473. North Holland, Amsterdam (1970)"},{"issue":"3","key":"199_CR15","doi-asserted-by":"crossref","first-page":"466","DOI":"10.2307\/2272731","volume":"37","author":"C. Parsons","year":"1972","unstructured":"Parsons C.: On n-quantifier induction. J. Symbolic Log. 37(3), 466\u2013482 (1972)","journal-title":"J. Symbolic Log."},{"key":"199_CR16","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/S0049-237X(08)70462-2","volume-title":"Logic Colloquium \u201984","author":"P. Pudl\u00e1k","year":"1986","unstructured":"Pudl\u00e1k P.: On the length of proofs of finitistic consistency statements in first-order theories. In: Paris, J.e.a. (eds) Logic Colloquium \u201984, pp. 165\u2013196. North-Holland, Amsterdam (1986)"},{"key":"199_CR17","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/S0049-237X(08)71124-8","volume-title":"Handbook of Mathematical Logic","author":"H. Schwichtenberg","year":"1977","unstructured":"Schwichtenberg H.: Some applications of cut-elimination. In: Barwise, J. (eds) Handbook of Mathematical Logic, pp. 867\u2013896. North Holland, Amsterdam (1977)"},{"key":"199_CR18","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/BF01621477","volume":"30","author":"W. Sieg","year":"1991","unstructured":"Sieg W.: Herbrand analyses. Arch. Math. Log. 30, 409\u2013441 (1991)","journal-title":"Arch. Math. Log."},{"key":"199_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59971-2","volume-title":"Subsystems of Second Order Arithmetic","author":"S.G. Simpson","year":"1999","unstructured":"Simpson S.G.: Subsystems of Second Order Arithmetic. Springer, Berlin (1999)"},{"key":"199_CR20","first-page":"302","volume-title":"From Frege to G\u00f6del","author":"T. Skolem","year":"1967","unstructured":"Skolem T.: The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains. In: Heijenoort, J.v. (eds) From Frege to G\u00f6del, pp. 302\u2013333. Harvard, Iuniverse (1967)"},{"key":"199_CR21","doi-asserted-by":"crossref","first-page":"524","DOI":"10.2307\/2026089","volume":"78","author":"W. Tait","year":"1981","unstructured":"Tait W.: Finitism. J. Philos. 78, 524\u2013546 (1981)","journal-title":"J. Philos."},{"key":"199_CR22","volume-title":"Proof Theory","author":"G. Takeuti","year":"1975","unstructured":"Takeuti G.: Proof Theory. North-Holland, Amsterdam (1975)"},{"key":"199_CR23","unstructured":"Visser, A.: Notes on I\u03a31 (1990?). Unpublished manuscript"},{"key":"199_CR24","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0168-0072(87)90066-2","volume":"35","author":"A. Wilkie","year":"1987","unstructured":"Wilkie A., Paris J.: On the scheme of induction for bounded arithmetic formulas. Ann. Pure Appl. Log. 35, 261\u2013302 (1987)","journal-title":"Ann. Pure Appl. Log."},{"key":"199_CR25","doi-asserted-by":"crossref","first-page":"942","DOI":"10.2307\/2275794","volume":"61","author":"D. Zambella","year":"1996","unstructured":"Zambella D.: Notes on polynomial bounded arithmetic. J. Symbolic Log. 61, 942\u2013966 (1996)","journal-title":"J. Symbolic Log."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-010-0199-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-010-0199-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-010-0199-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T11:00:21Z","timestamp":1711623621000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-010-0199-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,16]]},"references-count":25,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["199"],"URL":"https:\/\/doi.org\/10.1007\/s00153-010-0199-2","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,16]]}}}