{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T23:42:51Z","timestamp":1764373371488},"reference-count":18,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2004,2,3]],"date-time":"2004-02-03T00:00:00Z","timestamp":1075766400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets <jats:italic>B<\/jats:italic> such that <jats:italic>A<\/jats:italic> \u2286 <jats:italic>B<\/jats:italic> \u2286 acl(<jats:italic>A<\/jats:italic>) and closed subgroups of the Galois group Aut(acl(<jats:italic>A<\/jats:italic>)\/<jats:italic>A<\/jats:italic>). We also characterize when the topology of the Galois group is the quotient topology. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310083","type":"journal-article","created":{"date-parts":[[2004,2,4]],"date-time":"2004-02-04T13:02:17Z","timestamp":1075899737000},"page":"126-140","source":"Crossref","is-referenced-by-count":9,"title":["Weak forms of elimination of imaginaries"],"prefix":"10.1002","volume":"50","author":[{"given":"Enrique","family":"Casanovas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafel","family":"Farr\u00e9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,2,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061301000119"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01979940"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2586538"},{"key":"e_1_2_1_5_2","unstructured":"D.Haskell E.Hrushovski andD.Macpherson Definable sets in algebraically closed valued fields. Part I: Elimination of imaginaries. Preprint 2002."},{"key":"e_1_2_1_6_2","unstructured":"W.Hodges Model theory (Cambridge University Press Cambridge 1993)."},{"key":"e_1_2_1_7_2","unstructured":"E.Hrushovski PAC structures. Preprint 1991."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275911"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273140"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2694914"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760649"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"D.Marker Introduction to the model theory of fields. In: Model Theory of Fields (D. Marker M. Messmer and A. Pillay eds.) pp. 1\u201337 (Springer\u2010Verlag Berlin et al. 1996).","DOI":"10.1007\/978-3-662-22174-7_1"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"M.Messmer Some model theory of separably closed fields. In: Model Theory of Fields (D. Marker M. Messmer and A. Pillay eds.) pp. 135\u2013152 (Springer\u2010Verlag Berlin et al. 1996).","DOI":"10.1007\/978-3-662-22174-7_4"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274024"},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","unstructured":"A.Pillay Model theory of algebraically closed fields. In: Model Theory and Algebraic Geometry (E. Bouscaren ed.) pp. 61\u201384 (Springer\u2010Verlag Berlin 1998).","DOI":"10.1007\/978-3-540-68521-0_4"},{"key":"e_1_2_1_16_2","unstructured":"A.Pillay Model theory of difference fields. Lecture Notes Department ofMathematics University of Illinois at Urbana\u2010Champaign Spring 1999."},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273680"},{"key":"e_1_2_1_18_2","unstructured":"B.Poizat Cours de th\u00e9orie des mod\u00e8les (Nur al\u2010Mantiq wal\u2010Ma'rifah Villeurbanne 1985)."},{"key":"e_1_2_1_19_2","unstructured":"S.Shelah Classification theory (North\u2010Holland Publ. Comp. Amsterdam 1978)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310083","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T03:29:23Z","timestamp":1700191763000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310083"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,3]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["10.1002\/malq.200310083"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310083","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,3]]}}}