{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T15:56:46Z","timestamp":1775491006082,"version":"3.50.1"},"reference-count":8,"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 prove that every model of <jats:italic>T<\/jats:italic> = Th(\u03c9, &lt;,\u2026) (<jats:italic>T<\/jats:italic> countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049434_inline1\"\/> nonisomorphic countable models; and that if every model of <jats:italic>T<\/jats:italic> has an end extension, then every \u2223<jats:italic>T<\/jats:italic>\u2223-universal model of <jats:italic>T<\/jats:italic> has an end extension definable with parameters.<\/jats:p>","DOI":"10.2307\/2273531","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:48:21Z","timestamp":1146952101000},"page":"550-562","source":"Crossref","is-referenced-by-count":16,"title":["End extensions and numbers of countable models"],"prefix":"10.1017","volume":"43","author":[{"given":"Saharon","family":"Shelah","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049434_ref005","first-page":"331","volume-title":"Proceedings of the Tarski Symposium, Berkeley, 1971, Proceedings of Symposia in Pure Mathematics","volume":"XXV","author":"Keisler","year":"1974"},{"key":"S0022481200049434_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771640"},{"key":"S0022481200049434_ref003","volume-title":"Annals of Mathematical Logic","author":"Gaifman"},{"key":"S0022481200049434_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71505-2"},{"key":"S0022481200049434_ref008","volume-title":"Annals of Mathematical logic","author":"Shelah"},{"key":"S0022481200049434_ref006","first-page":"257","volume-title":"Infinitistic methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959","author":"MacDowell","year":"1961"},{"key":"S0022481200049434_ref001","first-page":"377","article-title":"Results concerning models of Peano arithmetic","volume":"12","author":"Gaifman","year":"1965","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200049434_ref007","first-page":"A","article-title":"On linearly ordered models and their end extensions","volume":"22","author":"Shelah","year":"1975","journal-title":"Notices of the American Mathematical Society"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049434","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T19:33:50Z","timestamp":1558985630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049434\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1978,9]]}},"alternative-id":["S0022481200049434"],"URL":"https:\/\/doi.org\/10.2307\/2273531","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,9]]}}}