{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:28:57Z","timestamp":1758274137993},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4940,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.<\/jats:p>","DOI":"10.2307\/2586686","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:41Z","timestamp":1146938561000},"page":"1014-1030","source":"Crossref","is-referenced-by-count":3,"title":["Undecidability of the real-algebraic structure of models of intuitionistic elementary analysis"],"prefix":"10.1017","volume":"65","author":[{"given":"Mikl\u00f3s","family":"Erd\u00e9lyi-Szab\u00f3","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011774_ref006","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19780242507"},{"key":"S0022481200011774_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90067-C"},{"key":"S0022481200011774_ref008","volume-title":"Annals of Pure and Applied Logic","author":"Scowcroft"},{"key":"S0022481200011774_ref005","volume-title":"The Foundations of Intuitionistic Mathematics","author":"Kleene","year":"1965"},{"key":"S0022481200011774_ref004","volume-title":"Intuitionism. An Introduction","author":"Heyting","year":"1956"},{"key":"S0022481200011774_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19980440305"},{"key":"S0022481200011774_ref001","first-page":"44\u201391","volume-title":"Model Theory of Algebra and Arithmetic","author":"Cherlin","year":"1980"},{"key":"S0022481200011774_ref010","first-page":"225\u2013339","volume-title":"Handbook of Philosophical Logic, Vol. III","author":"van Dalen","year":"1986"},{"key":"S0022481200011774_ref007","first-page":"194\u2013210","article-title":"Extending the topological interpretation to intuitionistic analysis","volume":"20","author":"Scott","year":"1968","journal-title":"Compositio Math."},{"key":"S0022481200011774_ref002","volume-title":"Mathematical Intuitionism: Introduction to Proof Theory","author":"Dragalin","year":"1987"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011774","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T20:47:48Z","timestamp":1557348468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011774\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S0022481200011774"],"URL":"https:\/\/doi.org\/10.2307\/2586686","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}