{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T07:54:59Z","timestamp":1648713299542},"reference-count":10,"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":12520,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,12]]},"abstract":"<jats:p>For <jats:italic>L<\/jats:italic> a countable first-order language, let <jats:italic>L(Q)<\/jats:italic> be logic with the quantifier <jats:italic>Qx<\/jats:italic> which means \u201cthere exist uncountably many <jats:italic>x<\/jats:italic>\u201d. We assume a little familiarity with Keisler's paper [8]. One finds there completeness and compactness theorems for <jats:italic>L(Q)<\/jats:italic>, as well as an omitting types theorem: a syntactic condition is given for a consistent countable theory to have a model satisfying \u2200<jats:italic>x<\/jats:italic>\u22c1\u03a3(<jats:italic>x<\/jats:italic>), where \u03a3 is a countable set of formulas of <jats:italic>L(Q)<\/jats:italic>. (See also Chang and Keisler [3] for the first-order omitting types theorem, due to Henkin and Orey.) An analogous theorem is proved in Barwise, Kaufmann, and Makkai [1] and in Kaufmann [6] for stationary logic. However, a more general theorem than just an anlaogue to Keisler's is proved there. Conditions are given which are sufficient for a theory <jats:italic>T<\/jats:italic> to have models satisfying sentences such as <jats:italic>aas<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>aas<\/jats:italic><jats:sub>2<\/jats:sub> \u2026 <jats:italic>aas<jats:sub>n<\/jats:sub><\/jats:italic>\u22c1\u03a3(<jats:italic>s<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026 <jats:italic>s<jats:sub>n<\/jats:sub><\/jats:italic>), \u2200<jats:italic>xaas<\/jats:italic> \u2228 \u03a3(<jats:italic>x, s<\/jats:italic>), and so forth. Bruce [2] had asked whether such a theorem can be proved for <jats:italic>L(Q)<\/jats:italic>. with \u201c<jats:italic>aa<\/jats:italic>\u201d replaced by \u201c<jats:italic>Q<\/jats:italic>*\u201d, where <jats:italic>Q<\/jats:italic>* is \u00ac<jats:italic>Q<\/jats:italic>\u00ac (\u201cfor all but countably many\u201d).<\/jats:p>","DOI":"10.2307\/2273290","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:51:21Z","timestamp":1146952281000},"page":"507-521","source":"Crossref","is-referenced-by-count":0,"title":["A new omitting types theorem for <i>L(Q)<\/i>"],"prefix":"10.1017","volume":"44","author":[{"given":"Matt","family":"Kaufmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048398_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90003-7"},{"key":"S0022481200048398_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200048398_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4843(70)80005-5"},{"key":"S0022481200048398_ref005","first-page":"A","article-title":"A new omitting types theorem for L(Q)","volume":"24","author":"Kaufmann","year":"1977","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200048398_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90019-5"},{"key":"S0022481200048398_ref010","volume-title":"A different proof of \u201cA new omitting types theorem for HQ)\u201d","author":"Wimmers","year":"1978"},{"key":"S0022481200048398_ref007","unstructured":"Kaufmann M. , Omitting types and L(Q), abstract of talk at 06, 1978 ASL meeting at Madison. Wisconsin, this Journal (to appear)."},{"key":"S0022481200048398_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90002-4"},{"key":"S0022481200048398_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4843(78)80001-1"},{"key":"S0022481200048398_ref006","unstructured":"Kaufmann M. , Some results in stationary logic. Doctoral dissertation, University of Wisconsin at Madison, 1978."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048398","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T20:27:47Z","timestamp":1558902467000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048398\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["S0022481200048398"],"URL":"https:\/\/doi.org\/10.2307\/2273290","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,12]]}}}