{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T23:49:04Z","timestamp":1720050544301},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":466,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the automorphism group of the algebraic closure of a substructure<jats:italic>A<\/jats:italic>of a pseudo-finite field<jats:italic>F<\/jats:italic>. We show that the behavior of this group, even when<jats:italic>A<\/jats:italic>is large, depends essentially on the roots of unity in<jats:italic>F<\/jats:italic>. For almost all completions of the theory of pseudofinite fields, we show that over<jats:italic>A<\/jats:italic>, algebraic closure agrees with definable closure, as soon as<jats:italic>A<\/jats:italic>contains the relative algebraic closure of the prime field.<\/jats:p>","DOI":"10.2178\/jsl.7704010","type":"journal-article","created":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T19:23:52Z","timestamp":1351884232000},"page":"1057-1066","source":"Crossref","is-referenced-by-count":4,"title":["On algebraic closure in pseudofinite fields"],"prefix":"10.1017","volume":"77","author":[{"given":"\u00d6zlem","family":"Beyarslan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ehud","family":"Hrushovski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001110_ref006","first-page":"151","volume-title":"Model theory and applications","volume":"11","author":"Hrushovski","year":"2002"},{"key":"S0022481200001110_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5673-9"},{"key":"S0022481200001110_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02498-8"},{"key":"S0022481200001110_ref009","volume-title":"Arithmetic algebraic geometry (Park City, UT, 1999)","author":"Tate","year":"2009"},{"key":"S0022481200001110_ref005","first-page":"838","volume":"59","author":"Hrushovski","year":"1994","journal-title":"Finitely axiomatizable \u21351 categorical theories"},{"key":"S0022481200001110_ref003","doi-asserted-by":"crossref","DOI":"10.1007\/b138352","volume-title":"Field arithmetic","volume":"11","author":"Fried","year":"2005"},{"key":"S0022481200001110_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-01-06001-4"},{"key":"S0022481200001110_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1970573"},{"key":"S0022481200001110_ref004","first-page":"601","volume-title":"Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften","volume":"116","author":"Hahn","year":"1907"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200001110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,15]],"date-time":"2020-07-15T12:57:00Z","timestamp":1594817820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200001110\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0022481200001110"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7704010","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}