{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T02:09:50Z","timestamp":1648951790440},"reference-count":7,"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":12611,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>T<\/jats:italic> be a complete countable first-order theory such that every ultrapower of a model of <jats:italic>T<\/jats:italic> is saturated. If <jats:italic>T<\/jats:italic> has a model omitting a type <jats:italic>p<\/jats:italic> in every cardinality &lt; \u2136<jats:sub>\u2032<\/jats:sub>, then <jats:italic>T<\/jats:italic> has a model omitting <jats:italic>p<\/jats:italic> in every cardinality. There is also a related theorem, and an example showing the \u2136<jats:sub>\u2032<\/jats:sub> cannot be improved.<\/jats:p>","DOI":"10.2307\/2273125","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:50:56Z","timestamp":1146937856000},"page":"319-324","source":"Crossref","is-referenced-by-count":4,"title":["Hanf number of omitting type for simple first-order theories"],"prefix":"10.1017","volume":"44","author":[{"given":"Saharon","family":"Shelah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048246_ref005","first-page":"576","article-title":"On the number of nonisomorphic models of a theory in a cardinality","volume":"17","author":"Shelah","year":"1970","journal-title":"abstract, Notices of the American Mathematical Society"},{"key":"S0022481200048246_ref001","first-page":"93","article-title":"Partition relations for cardinal numbers","volume":"16","author":"Erd\u00f6s","year":"1965","journal-title":"Acta Mathematica"},{"key":"S0022481200048246_ref004","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-10648"},{"key":"S0022481200048246_ref006","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200048246_ref003","first-page":"256","volume-title":"The theory of models, Proceedings of the Berkeley Symposium, 1962","author":"Morley","year":"1965"},{"key":"S0022481200048246_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90015-5"},{"key":"S0022481200048246_ref002","volume-title":"Model theory","author":"Chang","year":"1973"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048246","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T16:53:10Z","timestamp":1558889590000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048246\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1979,9]]}},"alternative-id":["S0022481200048246"],"URL":"https:\/\/doi.org\/10.2307\/2273125","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,9]]}}}