{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T09:57:29Z","timestamp":1772445449184,"version":"3.50.1"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1015,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give some sufficient conditions for a predicate <jats:italic>P<\/jats:italic> in a complete theory <jats:italic>T<\/jats:italic> to be \u201cstably embedded\u201d. Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200001894_inline1\"\/> be <jats:italic>P<\/jats:italic> with its \u201cinduced \u2205-definable structure\u201d. The conditions are that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200001894_inline1\"\/> (or rather its theory) is \u201crosy\u201d. <jats:italic>P<\/jats:italic> has <jats:italic>NIP<\/jats:italic> in <jats:italic>T<\/jats:italic> and that <jats:italic>P<\/jats:italic> is stably 1-embedded in <jats:italic>T<\/jats:italic>. This generalizes a recent result of Hasson and Onshuus [6] which deals with the case where <jats:italic>P<\/jats:italic> is o-minimal in <jats:italic>T<\/jats:italic>. Our proofs make use of the theory of strict nonforking and weight in <jats:italic>NIP<\/jats:italic> theories ([3], [10]).<\/jats:p>","DOI":"10.2178\/jsl\/1305810769","type":"journal-article","created":{"date-parts":[[2011,5,19]],"date-time":"2011-05-19T13:18:58Z","timestamp":1305811138000},"page":"665-672","source":"Crossref","is-referenced-by-count":6,"title":["Stable embeddedness and <i>NIP<\/i>"],"prefix":"10.1017","volume":"76","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001894_ref011","unstructured":"Usvyatsov A. , Morley sequences in dependent theories, preprint, http:\/\/arxiv.org\/abs\/0810.0733."},{"key":"S0022481200001894_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-009-0082-1"},{"key":"S0022481200001894_ref009","volume-title":"A course in model theory; an introduction to contemporary mathematical logic","author":"Poizat","year":"2000"},{"key":"S0022481200001894_ref006","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdp098"},{"key":"S0022481200001894_ref002","volume-title":"Archive for Mathematical Logic","author":"Adler"},{"key":"S0022481200001894_ref001","unstructured":"Adler H. , A geometric introduction to forking and thorn forking, 2007, preprint."},{"key":"S0022481200001894_ref003","unstructured":"Chernikov A. and Kaplan I. , Forking and dividing in NTP2 theories, to appear in this Journal, number 147 on the MODNET preprint server."},{"key":"S0022481200001894_ref007","unstructured":"Hrushovski E. and Pillay A. , On NIP and invariant measures, preprint 2009 (revised version), http:\/\/arxiv.org\/abs\/0710.2330."},{"key":"S0022481200001894_ref005","first-page":"919","volume":"72","author":"Ealy","year":"2007","journal-title":"Characterizing rosy theories"},{"key":"S0022481200001894_ref008","first-page":"1","volume":"71","author":"Onshuus","year":"2006","journal-title":"Properties and consequences of thorn independence"},{"key":"S0022481200001894_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2007.09.004"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200001894","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T08:30:48Z","timestamp":1556353848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200001894\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["S0022481200001894"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1305810769","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6]]}}}