{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T23:23:07Z","timestamp":1783984987077,"version":"3.55.0"},"reference-count":7,"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>We prove that in a continuous \u2135<jats:sub>0<\/jats:sub>-stable theory every type-definable group is definable. The two main ingredients in the proof are:<\/jats:p><jats:p>(i) Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and<\/jats:p><jats:p>(ii) Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.<\/jats:p>","DOI":"10.2178\/jsl\/1278682202","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"817-840","source":"Crossref","is-referenced-by-count":14,"title":["Definability of groups in \u2135<sub>0<\/sub>-stable metric structures"],"prefix":"10.1017","volume":"75","author":[{"given":"Ita\u00ef","family":"Ben Yaacov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002401_ref002","first-page":"829","volume":"70","author":"Yaacov","year":"2005","journal-title":"Uncountable dense categoricity in cats"},{"key":"S0022481200002401_ref006","volume-title":"Transactions of the American Mathematical Society","author":"Yaacov"},{"key":"S0022481200002401_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610004"},{"key":"S0022481200002401_ref004","first-page":"1111","volume":"75","author":"Yaacov","year":"2010","journal-title":"Stability and stable groups in continuous logic"},{"key":"S0022481200002401_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm179-3-2"},{"key":"S0022481200002401_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s11813-008-0009-x"},{"key":"S0022481200002401_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735219.011"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002401","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:39:15Z","timestamp":1556401155000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002401\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002401"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682202","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}