{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T09:33:03Z","timestamp":1763544783147},"reference-count":50,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,9,5]],"date-time":"2014-09-05T00:00:00Z","timestamp":1409875200000},"content-version":"unspecified","delay-in-days":369,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log"],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Edward Nelson published in 1986 a book defending an extreme formalist view of mathematics according to which there is an<jats:italic>impassable barrier<\/jats:italic>in the totality of exponentiation. On the positive side, Nelson embarks on a program of investigating how much mathematics can be interpreted in Raphael Robinson's theory of arithmetic<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600010660_inline1\" \/>. In the shadow of this program, some very nice logical investigations and results were produced by a number of people, not only regarding what can be interpreted in<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600010660_inline1\" \/>but also what cannot be so interpreted. We explain some of these results and rely on them to discuss Nelson's position.<\/jats:p>","DOI":"10.1017\/s1079898600010660","type":"journal-article","created":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T08:31:15Z","timestamp":1469694675000},"page":"289-317","source":"Crossref","is-referenced-by-count":9,"title":["Interpretability in Robinson's Q"],"prefix":"10.1017","volume":"19","author":[{"given":"Fernando","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Gilda","family":"Ferreira","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,9,5]]},"reference":[{"key":"S1079898600010660_ref047","doi-asserted-by":"crossref","DOI":"10.1515\/9783112451144","volume-title":"Das Kontinuum","author":"Weyl","year":"1918"},{"key":"S1079898600010660_ref046","volume-title":"What if current foundations of mathematics are inconsistent?","author":"Voevodsky","year":"2010"},{"key":"S1079898600010660_ref028","doi-asserted-by":"publisher","DOI":"10.1515\/9781400858927"},{"key":"S1079898600010660_ref042","volume-title":"Undecidable theories","author":"Tarski","year":"1953"},{"key":"S1079898600010660_ref010","doi-asserted-by":"publisher","DOI":"10.4064\/fm-49-1-35-92"},{"key":"S1079898600010660_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/s001530200004"},{"key":"S1079898600010660_ref048","first-page":"329","volume-title":"Logic colloquium 1984","author":"Wilikie","year":"1986"},{"key":"S1079898600010660_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/2269764"},{"key":"S1079898600010660_ref040","volume-title":"Letter to P. Haj\u00e9k","author":"Solovay","year":"1976"},{"key":"S1079898600010660_ref005","unstructured":"Buss S. R. , Bounded arithmetic, Ph.D. thesis, Princeton University, 1985, a revision of this thesis was published by Bibliopolis (Naples) in 1986."},{"key":"S1079898600010660_ref034","doi-asserted-by":"publisher","DOI":"10.2307\/2274231"},{"key":"S1079898600010660_ref015","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150098"},{"key":"S1079898600010660_ref029","unstructured":"Nelson E. , Confessions of an apostate mathematician, paper available at https:\/\/web.math.princeton.edu\/~nelson\/papers.html, 1995."},{"key":"S1079898600010660_ref036","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12013-2"},{"key":"S1079898600010660_ref043","first-page":"307","volume-title":"Mathematical logic","author":"Visser","year":"1990"},{"key":"S1079898600010660_ref050","doi-asserted-by":"publisher","DOI":"10.2307\/2275794"},{"key":"S1079898600010660_ref023","doi-asserted-by":"publisher","DOI":"10.4169\/000298910x480063"},{"key":"S1079898600010660_ref020","unstructured":"Ferreira G. , Aritm\u00e9tica comput\u00e1vel em espa\u00e7o polinomial, Master's thesis, Universidade de Lisboa, 2001, (in Portuguese)."},{"key":"S1079898600010660_ref030","unstructured":"Nelson E. , Completed versus incomplete infinity in arithmetic, paper available at https:\/\/web.math.princeton.edu\/~nelson\/papers.html, 2005."},{"key":"S1079898600010660_ref026","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511529948"},{"key":"S1079898600010660_ref006","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1515\/9781400865253.183","volume-title":"Diffusion, quantum theory, and radically elementary mathematics","author":"Buss","year":"2006"},{"key":"S1079898600010660_ref035","first-page":"729","article-title":"An essentially undecidable axiom system","volume":"1","author":"Robinson","year":"1952","journal-title":"Proceedings of the International Congress of Mathematicians, Cambridge 1950"},{"key":"S1079898600010660_ref044","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370389"},{"key":"S1079898600010660_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420123"},{"key":"S1079898600010660_ref024","first-page":"185","volume-title":"Arithmetic, proof theory and computational complexity","author":"H\u00e1jek","year":"1993"},{"key":"S1079898600010660_ref045","doi-asserted-by":"publisher","DOI":"10.1007\/BF01387407"},{"key":"S1079898600010660_ref021","unstructured":"Ferreira G. , Sistemas de an\u00e1lise fraca para a integra\u00e7\u00e3o, Ph.D. thesis, Universidade de Lisboa, 2006, (in Portuguese)."},{"key":"S1079898600010660_ref027","volume-title":"Model theory: An introduction","volume":"217","author":"Marker","year":"2002"},{"key":"S1079898600010660_ref038","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S1079898600010660_ref049","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90066-2"},{"key":"S1079898600010660_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2275924"},{"key":"S1079898600010660_ref031","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976889.005"},{"key":"S1079898600010660_ref016","unstructured":"Ferreira F. , Polynomial time computable arithmetic and conservative extensions, Ph.D. thesis, Pennsylvania State University, USA, 1988."},{"key":"S1079898600010660_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"S1079898600010660_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201998"},{"key":"S1079898600010660_ref003","unstructured":"Bennett J. , On spectra, Ph.D. thesis, Princeton University, Princeton, New Jersey, 1962."},{"key":"S1079898600010660_ref039","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71123-6"},{"key":"S1079898600010660_ref017","first-page":"161","volume-title":"Logic and computation","author":"Ferreira","year":"1990"},{"key":"S1079898600010660_ref033","first-page":"294","article-title":"Les math\u00e9matiques et la logique","volume":"14","author":"Poincar\u00e9","year":"1906","journal-title":"Revue de m\u00e9taphysic et de moral"},{"key":"S1079898600010660_ref008","unstructured":"Dimitracopoulos C. , Matiyasevi\u010d theorem and fragments of arithmetic, Ph.D. thesis, University of Manchester, 1980."},{"key":"S1079898600010660_ref004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1305\/ndjfl\/1039293018","article-title":"Predicative logic and formal arithmetic","volume":"39","author":"Burgess","year":"1998","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1079898600010660_ref012","unstructured":"Fernandes A. 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