{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T01:40:16Z","timestamp":1773970816711,"version":"3.50.1"},"reference-count":5,"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":2749,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius <jats:italic>r<\/jats:italic> &lt; 1 contained in the valuation ring and the set of balls of a given multiplicative radius <jats:italic>r<\/jats:italic> &lt; 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and only if its algebraic closure is stably embedded.<\/jats:p>","DOI":"10.2178\/jsl\/1154698580","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:23:20Z","timestamp":1198081400000},"page":"831-862","source":"Crossref","is-referenced-by-count":2,"title":["Stable embeddedness in algebraically closed valued fields"],"prefix":"10.1017","volume":"71","author":[{"given":"E.","family":"Hrushovski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Tatarsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005958_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65505-0"},{"key":"S0022481200005958_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758643"},{"key":"S0022481200005958_ref005","volume-title":"Complete theories","author":"Robinson","year":"1956"},{"key":"S0022481200005958_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02498-8"},{"key":"S0022481200005958_ref003","volume-title":"Journal f\u00fcr die reine und angewandte Mathematik","author":"Haskell"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005958","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T19:54:31Z","timestamp":1556826871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005958\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,9]]}},"alternative-id":["S0022481200005958"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1154698580","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,9]]}}}