{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T15:50:11Z","timestamp":1715269811883},"reference-count":13,"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":4759,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that any 1-closed (see def 1.1) model of the \u03a0<jats:sub>2<\/jats:sub> consequences of PA satisfies \u00ac<jats:italic>Cons<\/jats:italic> PA which gives a proof of the second G\u00f6del incompleteness theorem without the use of the G\u00f6del diagonal lemma. We prove a few other theorems by the same method.<\/jats:p>","DOI":"10.2307\/2694926","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:03:53Z","timestamp":1146938633000},"page":"349-356","source":"Crossref","is-referenced-by-count":15,"title":["Existentially closed structures and G\u00f6del's second incompleteness theorem"],"prefix":"10.1017","volume":"66","author":[{"given":"Zofia","family":"Adamowicz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Teresa","family":"Bigorajska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011361_ref013","first-page":"111","article-title":"A new proof of the G\u00f6del's result of non-provability of consistency","volume":"14","author":"Vopenka","year":"1966","journal-title":"L'Acad\u00e9mie Polonaise des Sciences. Bulletin. S\u00e9rie des Sciences Math\u00e9matiques"},{"key":"S0022481200011361_ref010","first-page":"285","volume":"61","author":"Kotlarski","year":"1996","journal-title":"An addition to rosser's theorem"},{"key":"S0022481200011361_ref009","first-page":"1414","volume":"59","author":"Kotlarski","year":"1994","journal-title":"On the incompleteness theorems"},{"key":"S0022481200011361_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050074"},{"key":"S0022481200011361_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19940400409"},{"key":"S0022481200011361_ref006","first-page":"311","article-title":"On G\u00f6del second incompleteness theorem","volume":"121","author":"Jech","year":"1994","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200011361_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01622877"},{"key":"S0022481200011361_ref003","unstructured":"Cie\u015blinski C. , G\u00f6dels incompleteness theorems and semantical antinomies, Ph.D. thesis , Warsaw University, 1999."},{"key":"S0022481200011361_ref002","first-page":"388","article-title":"A new proof of the G\u00f6del incompleteness theorem","volume":"36","author":"Boolos","year":"1989","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200011361_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S0022481200011361_ref011","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19980440406"},{"key":"S0022481200011361_ref012","doi-asserted-by":"crossref","unstructured":"Smorynski C. , The incompleteness theorem, (J. Barwise, editor), Handbook of Mathematical Logic, North Holland Publishing Company, Amsterdam, 1977, pp. 821\u2013865.","DOI":"10.1016\/S0049-237X(08)71123-6"},{"key":"S0022481200011361_ref001","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032541"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T00:46:41Z","timestamp":1557276401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011361\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,3]]}},"alternative-id":["S0022481200011361"],"URL":"https:\/\/doi.org\/10.2307\/2694926","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,3]]}}}