{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T20:28:45Z","timestamp":1775507325071,"version":"3.50.1"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12976,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>T<\/jats:italic> be a complete theory with infinite models in a countable language. The stability function <jats:italic>g<jats:sub>T<\/jats:sub><\/jats:italic>(\u03ba) is defined as the supremum of the number of types over models of <jats:italic>T<\/jats:italic> of power \u03ba. It is proved that there are only six possible stability functions, namely \u03ba, \u03ba + 2<jats:sup>\u03c9<\/jats:sup>, \u03ba<jats:sup>\u03c9<\/jats:sup>, ded \u03ba, (ded \u03ba)<jats:sup>\u03c9<\/jats:sup>, 2<jats:sup>\u03ba<\/jats:sup>.<\/jats:p>","DOI":"10.2307\/2273523","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:48:21Z","timestamp":1146952101000},"page":"481-486","source":"Crossref","is-referenced-by-count":2,"title":["The stability function of a theory"],"prefix":"10.1017","volume":"43","author":[{"given":"H. Jerome","family":"Keisler","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049355_ref002","first-page":"157","article-title":"Some remarks on set theory, X","volume":"1","author":"Erd\u00f6s","year":"1966","journal-title":"Studia Scientiarum Mathematicarum Hungarica"},{"key":"S0022481200049355_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0175782-0"},{"key":"S0022481200049355_ref003","first-page":"A","article-title":"The number of types in a first order theory","volume":"21","author":"Keisler","year":"1974","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200049355_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018541"},{"key":"S0022481200049355_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90015-5"},{"key":"S0022481200049355_ref001","volume-title":"Model theory","author":"Chang","year":"1973"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049355","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T19:33:37Z","timestamp":1558985617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049355\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1978,9]]}},"alternative-id":["S0022481200049355"],"URL":"https:\/\/doi.org\/10.2307\/2273523","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,9]]}}}