{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T23:02:57Z","timestamp":1768690977965,"version":"3.49.0"},"reference-count":37,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T00:00:00Z","timestamp":1523923200000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["155136"],"award-info":[{"award-number":["155136"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A new case of Shelah's eventual categoricity conjecture is established:\n<jats:disp-quote content-type=\"quotation\"><jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0001\"\/> be an abstract elementary class with amalgamation. Write <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0002\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0003\"\/>. Assume that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0004\"\/> is <jats:italic>H<\/jats:italic><jats:sub>2<\/jats:sub>\u2010tame and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0005\"\/> has primes over sets of the form <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0006\"\/>. If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0007\"\/> is categorical in some <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0008\"\/>, then <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0009.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0009\"\/> is categorical in all <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0010.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0010\"\/>.<\/jats:p><\/jats:disp-quote>\nThe result had previously been established when the stronger locality assumptions of full tameness and shortness are also required. An application of the method of proof of the mentioned result is that Shelah's categoricity conjecture holds in the context of homogeneous model theory (this was known, but our proof gives new cases): If <jats:italic>D<\/jats:italic> be a homogeneous diagram in a first\u2010order theory <jats:italic>T<\/jats:italic> and <jats:italic>D<\/jats:italic> is categorical in a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0011.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0011\"\/>, then <jats:italic>D<\/jats:italic> is categorical in all <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500068-math-0012.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500068:malq201500068-math-0012\"\/>.<\/jats:p>","DOI":"10.1002\/malq.201500068","type":"journal-article","created":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T17:44:34Z","timestamp":1523987074000},"page":"25-36","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes"],"prefix":"10.1002","volume":"64","author":[{"given":"Sebastien","family":"Vasey","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences Carnegie Mellon University Wean Hall 6113 Pittsburgh PA 15213 United States of America"},{"name":"Department of Mathematics Harvard University, Science Center One Oxford Street Cambridge MA 02138 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,4,17]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/050"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1153858652"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1230396746"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2014.30"},{"key":"e_1_2_7_6_1","unstructured":"W.Boney Tameness in groups and similar AECs in preparation."},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2017.02.002"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2017.01.005"},{"key":"e_1_2_7_9_1","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1201\/9781315368078-13","volume-title":"Beyond First Order Model Theory","author":"Boney W.","year":"2017"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-017-0532-0"},{"key":"e_1_2_7_11_1","unstructured":"W.BoneyandS.Vasey Good frames in the Hart\u2010Shelah example to appear in Arch. 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