{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T15:31:59Z","timestamp":1697643119365},"reference-count":2,"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":12976,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a model of Peano arithmetic in an uncountable language which has no elementary end extension. This answers a question of Gaifman and contrasts with the well-known theorem of MacDowell and Specker which states that every model of Peano arithmetic in a countable language has an elementary end extension. The construction employs forcing in a nonstandard model.<\/jats:p>","DOI":"10.2307\/2273532","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:48:21Z","timestamp":1146937701000},"page":"563-567","source":"Crossref","is-referenced-by-count":5,"title":["A model of peano arithmetic with no elementary end extension"],"prefix":"10.1017","volume":"43","author":[{"given":"George","family":"Mills","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049446_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90002-4"},{"key":"S0022481200049446_ref002","first-page":"257","volume-title":"Infinitistic Methods, Proceedings of the Symposium on Foundations of Mathematics","author":"MacDowell","year":"1959"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T15:33:22Z","timestamp":1558971202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049446\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,9]]},"references-count":2,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1978,9]]}},"alternative-id":["S0022481200049446"],"URL":"https:\/\/doi.org\/10.2307\/2273532","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,9]]}}}