{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T09:57:54Z","timestamp":1648547874667},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8412,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Basic results on the model theory of substructures of a fixed model are presented. The main point is to avoid the use of the compactness theorem, so this work can easily be applied to the model theory of <jats:italic>L<\/jats:italic><jats:sub><jats:italic>\u03c9<\/jats:italic>1,<jats:italic>\u03c9<\/jats:italic><\/jats:sub> and its relatives. Among other things we prove the following theorem:<\/jats:p><jats:p>Let <jats:italic>M<\/jats:italic> be a model, and let <jats:italic>\u03bb<\/jats:italic> be a cardinal satisfying <jats:italic>\u03bb<\/jats:italic><jats:sup>\u2223<jats:italic>L<\/jats:italic>(<jats:italic>M<\/jats:italic>)\u2223<\/jats:sup> = <jats:italic>\u03bb<\/jats:italic>. If <jats:italic>M<\/jats:italic> does not have the <jats:italic>\u03c9<\/jats:italic>-order property, then for every <jats:italic>A<\/jats:italic> \u2286 <jats:italic>M<\/jats:italic>, \u2223<jats:italic>A<\/jats:italic>\u2223 \u2264 <jats:italic>\u03bb<\/jats:italic>, and every <jats:bold>I<\/jats:bold> \u2286 <jats:italic>M<\/jats:italic> of cardinality <jats:italic>\u03bb<\/jats:italic><jats:sup>+<\/jats:sup> there exists <jats:bold>J<\/jats:bold> \u2286 <jats:bold>I<\/jats:bold> cardinality <jats:italic>\u03bb<\/jats:italic><jats:sup>+<\/jats:sup> which is an indiscernible set over <jats:italic>A<\/jats:italic>.<\/jats:p><jats:p>This is an improvement of a result of S. Shelah.<\/jats:p>","DOI":"10.2307\/2274908","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:38:25Z","timestamp":1146940705000},"page":"115-123","source":"Crossref","is-referenced-by-count":2,"title":["Indiscernible sequences in a model which fails to have the order property"],"prefix":"10.1017","volume":"56","author":[{"given":"Rami","family":"Grossberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024944_ref001","first-page":"124","volume":"56","author":"Grossberg","year":"1991","journal-title":"On chains of relatively saturated submodels of a model without the order property"},{"key":"S0022481200024944_ref002","first-page":"302","volume":"51","author":"Grossbery","year":"1986","journal-title":"The number of nonisomorphic models of an infinitary theory which has the order property"},{"key":"S0022481200024944_ref007","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BFb0098511","volume-title":"Around classification theory of models","volume":"1182","author":"Shelah","year":"1987"},{"key":"S0022481200024944_ref004","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200024944_ref005","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/BFb0082242","volume-title":"I, Classification theory","volume":"1292","author":"Shelah","year":"1988"},{"key":"S0022481200024944_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02762619"},{"key":"S0022481200024944_ref006","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1972.41.247"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024944","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T18:36:13Z","timestamp":1558118173000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024944\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,3]]}},"alternative-id":["S0022481200024944"],"URL":"https:\/\/doi.org\/10.2307\/2274908","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,3]]}}}