{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T11:48:26Z","timestamp":1773834506575,"version":"3.50.1"},"reference-count":16,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T00:00:00Z","timestamp":1375747200000},"content-version":"vor","delay-in-days":5,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Hungarian National Foundation for Scientific Research","award":["K68262"],"award-info":[{"award-number":["K68262"]}]},{"name":"Hungarian National Foundation for Scientific Research","award":["K83726"],"award-info":[{"award-number":["K83726"]}]},{"name":"Jnos Bolyai Research Scholarship of the Hungarian Academy of Sciences"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p>By a celebrated theorem of Morley, a theory <jats:italic>T<\/jats:italic> is \u2135<jats:sub>1<\/jats:sub>\u2010categorical if and only if it is \u03ba\u2010categorical for all uncountable \u03ba. In this paper we are taking the first steps towards extending Morley's categoricity theorem \u201cto the finite\u201d. In more detail, we are presenting conditions, implying that certain finite subsets of certain \u2135<jats:sub>1<\/jats:sub>\u2010categorical <jats:italic>T<\/jats:italic> have at most one <jats:italic>n<\/jats:italic>\u2010element model for each natural number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201110048-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:malq201110048:equation:malq201110048-math-0001\"\/> (counting up to isomorphism, of course).<\/jats:p>","DOI":"10.1002\/malq.201110048","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T11:35:31Z","timestamp":1375788931000},"page":"303-331","source":"Crossref","is-referenced-by-count":4,"title":["Upward Morley's theorem downward"],"prefix":"10.1002","volume":"59","author":[{"given":"G\u00e1bor","family":"S\u00e1gi","sequence":"first","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics Hungarian Academy of Sciences, Re\u00e1ltanoda u. 13\u201015  1053 Budapest Hungary"},{"name":"Matematika Int\u00e9zet, Budapesti M\u0171szaki \u00e9s Gazdas\u00e1gtudomnyi Egyetem, Pf. 91  1521 Budapest Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zal\u00e1n","family":"Gyenis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and its Applications Central European University, Nador u. 9  1051 Budapest Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2013,8,6]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Model Theory, Studies in Logic and the Foundations of Mathematics","author":"Chang C. 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