{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:27:02Z","timestamp":1772267222124,"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":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Building on Hrushovski's work in [5], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite internal covers. We introduce the notion of retractability of a definable groupoid (which is slightly stronger than Hrushovski's notion of eliminability), give some criteria for when groupoids are retractable, and show how retractability relates to both 3-uniqueness and the splitness of finite internal covers. One application we give is a new direct method of constructing non-eliminable groupoids from witnesses to the failure of 3-uniqueness. Another application is a proof that any finite internal cover of a stable theory with a centerless liaison groupoid is almost split.<\/jats:p>","DOI":"10.2178\/jsl\/1278682207","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"905-929","source":"Crossref","is-referenced-by-count":5,"title":["Groupoids, covers, and 3-uniqueness in stable theories"],"prefix":"10.1017","volume":"75","author":[{"given":"John","family":"Goodrick","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexei","family":"Kolesnikov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002450_ref006","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534372.001.0001","volume-title":"Geometric stability theory","author":"Pillay","year":"1996"},{"key":"S0022481200002450_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02498-8"},{"key":"S0022481200002450_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90046-5"},{"key":"S0022481200002450_ref005","unstructured":"Hrushovski Ehud , Groupoids, imaginaries and internal covers, preprint. arXiv: math. LO\/0603413."},{"key":"S0022481200002450_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00018-3"},{"key":"S0022481200002450_ref002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061306000530"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002450","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T05:39:33Z","timestamp":1711604373000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002450\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002450"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682207","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}