{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T11:46:32Z","timestamp":1710503192199},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2658,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>V<\/jats:italic> be the cumulative set theoretic hierarchy, generated from the empty set by taking powers at successor stages and unions at limit stages and. following [2], let the primitive language of set theory be the first order language which contains binary symbols for equality and membership only. Despite the existence of \u2200\u2200-formulae in the primitive language, with two free variables, which are satisfiable in \u2200 but not by finite sets ([5]). and therefore of \u2203\u2203\u2200\u2200 sentences of the same language, which are undecidable in ZFC without the Axiom of Infinity, truth in <jats:italic>V<\/jats:italic> for \u2203*\u2200\u2200-sentences of the primitive language, is decidable ([1]). Completeness of <jats:italic>ZF<\/jats:italic> with respect to such sentences follows.<\/jats:p>","DOI":"10.2178\/jsl\/1164060452","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T11:24:03Z","timestamp":1198063443000},"page":"1200-1222","source":"Crossref","is-referenced-by-count":12,"title":["Truth In V for \u2203*\u2200\u2200-Sentences is Decidable"],"prefix":"10.1017","volume":"71","author":[{"given":"D.","family":"Bell\u00e9","sequence":"first","affiliation":[]},{"given":"F.","family":"Parlamento","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005739_ref005","first-page":"285","article-title":"Note on: The logically simplest form of the infinity axiom","volume":"108","author":"Parlamento","year":"1990","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200005739_ref001","unstructured":"Bell\u00e8 D. , The decision problem for extensional set theories, Ph.D. thesis , Universit\u00e0di Siena, 1998."},{"key":"S0022481200005739_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19780241902"},{"key":"S0022481200005739_ref004","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420105"},{"key":"S0022481200005739_ref006","first-page":"1230","volume":"56","author":"Parlamento","year":"1991","journal-title":"Expressing infinity without foundation"},{"key":"S0022481200005739_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03630-7"},{"key":"S0022481200005739_ref002","doi-asserted-by":"publisher","DOI":"10.4064\/fm177-3-3"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005739","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T15:29:47Z","timestamp":1556810987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005739\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["S0022481200005739"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1164060452","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}