{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T18:00:19Z","timestamp":1759341619003},"reference-count":6,"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":5398,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p><jats:underline>Saturation is (<jats:italic>\u03bc<\/jats:italic>, <jats:italic>\u03ba<\/jats:italic>)-transferable in <jats:italic>T<\/jats:italic><\/jats:underline> if and only if there is an expansion <jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub> of <jats:italic>T<\/jats:italic> with |<jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub>| = |<jats:italic>T<\/jats:italic>| such that if <jats:italic>M<\/jats:italic> is a \u03bc-saturated model of <jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub> and |<jats:italic>M<\/jats:italic>| \u2265 <jats:italic>\u03ba<\/jats:italic> then the reduct <jats:italic>M<\/jats:italic>|<jats:italic>L(T)<\/jats:italic> is <jats:italic>\u03ba<\/jats:italic>-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (\u2135<jats:sub>0<\/jats:sub>, <jats:italic>\u03bb<\/jats:italic>)-transferable or (<jats:italic>\u03ba<\/jats:italic>(<jats:italic>T<\/jats:italic>), <jats:italic>\u03bb<\/jats:italic>)-transferable for all <jats:italic>\u03bb<\/jats:italic>. Further if for some <jats:italic>\u03bc<\/jats:italic> \u2265 |<jats:italic>T<\/jats:italic>|,2<jats:sup><jats:italic>\u03bc<\/jats:italic><\/jats:sup> &gt; <jats:italic>\u03bc<\/jats:italic><jats:sup>+<\/jats:sup>, stability is equivalent to for all \u03bc \u2265 |<jats:italic>T<\/jats:italic>|, saturation is (<jats:italic>\u03bc<\/jats:italic>, 2<jats:sup><jats:italic>\u03bc<\/jats:italic><\/jats:sup>)-transferable.<\/jats:p>","DOI":"10.2307\/2586492","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:03:01Z","timestamp":1146938581000},"page":"678-684","source":"Crossref","is-referenced-by-count":2,"title":["Transfering saturation, the finite cover property, and stability"],"prefix":"10.1017","volume":"64","author":[{"given":"John T.","family":"Baldwin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rami","family":"Grossberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200013542_ref006","volume-title":"Classification Theory and the Number of Nonisomorphic Models","author":"Shelah","year":"1990"},{"key":"S0022481200013542_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90015-5"},{"key":"S0022481200013542_ref003","first-page":"23\u201346","volume":"32","author":"Keisler","year":"1967","journal-title":"Ultraproducts which are not saturated"},{"key":"S0022481200013542_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0314619-7"},{"key":"S0022481200013542_ref001","first-page":"673\u2013683","volume":"60","author":"Casanovas","year":"1995","journal-title":"Compactly expandable models and stability"},{"key":"S0022481200013542_ref002","volume-title":"Model Theory","author":"Chang","year":"1990"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200013542","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T21:17:33Z","timestamp":1557436653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200013542\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,6]]}},"alternative-id":["S0022481200013542"],"URL":"https:\/\/doi.org\/10.2307\/2586492","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}