{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T17:42:51Z","timestamp":1648921371395},"reference-count":11,"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":6585,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Assume <jats:italic>T<\/jats:italic> is stable, small and \u03a6(<jats:italic>x<\/jats:italic>) is a formula of <jats:italic>L<\/jats:italic>(<jats:italic>T<\/jats:italic>). We study the impact on <jats:italic>T<\/jats:italic>\u2308\u03a6 of naming finitely many elements of a model of <jats:italic>T<\/jats:italic>. We consider the cases of <jats:italic>T<\/jats:italic>\u2308\u03a6 which is <jats:italic>\u03c9<\/jats:italic>-stable or superstable of finite rank. In these cases we prove that if <jats:italic>T<\/jats:italic> has <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017801_inline1\" \/> countable models and <jats:italic>Q<\/jats:italic> = \u03a6(<jats:italic>M<\/jats:italic>) is countable and atomic or saturated, then any good type in <jats:italic>S<\/jats:italic>(<jats:italic>Q<\/jats:italic>) is <jats:italic>\u03c4<\/jats:italic>-stable. If <jats:italic>T<\/jats:italic>\u2308\u03a6 is <jats:italic>\u03c9<\/jats:italic>-stable and (bounded, 1-based or of finite rank) with <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017801_inline2\" \/>, then we prove that every good <jats:italic>p<\/jats:italic> \u2208 <jats:italic>S<\/jats:italic>(<jats:italic>Q<\/jats:italic>) is <jats:italic>\u03c4<\/jats:italic>-stable for any countable <jats:italic>Q<\/jats:italic>. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories.<\/jats:p>","DOI":"10.2307\/2275614","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:57:36Z","timestamp":1146956256000},"page":"318-333","source":"Crossref","is-referenced-by-count":2,"title":["On atomic or saturated sets"],"prefix":"10.1017","volume":"61","author":[{"given":"Ludomir","family":"Newelski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017801_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1983-0715871-9"},{"key":"S0022481200017801_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760651"},{"key":"S0022481200017801_ref009","volume-title":"Classification theory","author":"Shelah","year":"1990"},{"key":"S0022481200017801_ref006","first-page":"648","volume":"58","author":"Newelski","year":"1993","journal-title":"Scott analysis of pseudo-types"},{"key":"S0022481200017801_ref005","first-page":"644","volume":"57","author":"Newelski","year":"1992","journal-title":"A model and its subset"},{"key":"S0022481200017801_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm-81-2-133-145"},{"key":"S0022481200017801_ref003","unstructured":"Buechler S. , Vaught's conjecture for superstable theories of finite rank, preprint, 10 1993."},{"key":"S0022481200017801_ref002","first-page":"377","volume":"48","author":"Bouscaren","year":"1983","journal-title":"Countable models of multidimensional \u21350-stable theories"},{"key":"S0022481200017801_ref001","volume-title":"Fundamentals of stability theory","author":"Baldwin","year":"1987"},{"key":"S0022481200017801_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90044-8"},{"key":"S0022481200017801_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90028-0"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017801","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T19:07:21Z","timestamp":1557774441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017801\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S0022481200017801"],"URL":"https:\/\/doi.org\/10.2307\/2275614","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}