{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:05:37Z","timestamp":1759147537008},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1472,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasi-finitization of the infinite pigeonhole principle IPP, arriving at the \u201cfinitary\u201d infinite pigeonhole principle FIPP<jats:sub>1<\/jats:sub>. That turned out to not be the proper formulation and so we proposed an alternative version FIPP<jats:sub>2<\/jats:sub>. Tao himself formulated yet another version FIPP<jats:sub>3<\/jats:sub> in a revised version of his essay.<\/jats:p><jats:p>We give a counterexample to FIPP<jats:sub>1<\/jats:sub> and discuss for both of the versions FIPP<jats:sub>2<\/jats:sub> and FIPP<jats:sub>3<\/jats:sub> the faithfulness of their respective finitization of IPP by studying the equivalences IPP \u2194 FIPP<jats:sub>2<\/jats:sub> and IPP \u2194 FIPP<jats:sub>3<\/jats:sub> in the context of reverse mathematics ([9]). In the process of doing this we also introduce a continuous uniform boundedness principle CUB as a formalization of Tao's notion of a correspondence principle and study the strength of this principle and various restrictions thereof in terms of reverse mathematics, i.e., in terms of the \u201cbig five\u201d subsystems of second order arithmetic.<\/jats:p>","DOI":"10.2178\/jsl\/1264433926","type":"journal-article","created":{"date-parts":[[2010,1,25]],"date-time":"2010-01-25T15:38:59Z","timestamp":1264433939000},"page":"355-371","source":"Crossref","is-referenced-by-count":5,"title":["On Tao's \u201cfinitary\u201d infinite pigeonhole principle"],"prefix":"10.1017","volume":"75","author":[{"given":"Jaime","family":"Gaspar","sequence":"first","affiliation":[]},{"given":"Ulrich","family":"Kohlenbach","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003005_ref012","volume-title":"Constructivism in mathematics. Vol. I and II","author":"Troelstra","year":"1988"},{"key":"S0022481200003005_ref011","unstructured":"Tao Terence , The correspondence principle and finitary ergodic theory, http:\/\/terrytao.wordpress.com, 2008."},{"key":"S0022481200003005_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22110-5_5"},{"key":"S0022481200003005_ref003","unstructured":"Hirst Jeffry L. , Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University, 1987."},{"key":"S0022481200003005_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.11.001"},{"key":"S0022481200003005_ref001","first-page":"47","volume-title":"Reverse mathematics 2001","volume":"21","author":"Brown","year":"2005"},{"key":"S0022481200003005_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050055"},{"key":"S0022481200003005_ref010","unstructured":"Tao Terence , Soft analysis, hardanalysis, and thefinite convergence principle, http:\/\/terrytao.wordpress.com, 2007, Appeared in \u201cT. Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, pp. 298, 2008.\u201d."},{"key":"S0022481200003005_ref007","first-page":"81","volume-title":"Proceedings of the 13th Workshop on Logic, Language, Information and Computation (WoLLIC 2006)","volume":"165","author":"Kohlenbach","year":"2006"},{"key":"S0022481200003005_ref008","volume-title":"Applied proof theory: proof interpretations and their use in mathematics","author":"Kohlenbach","year":"2008"},{"key":"S0022481200003005_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S0022481200003005_ref006","first-page":"92","volume-title":"Reflections on the foundations of mathematics: Essays in Honor of Solomon Feferman","volume":"15","author":"Kohlenbach","year":"2002"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003005","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T20:37:13Z","timestamp":1556483833000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003005\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["S0022481200003005"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1264433926","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}