{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T10:22:18Z","timestamp":1706178138266},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3663,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A compact complex space <jats:italic>X<\/jats:italic> is viewed as a 1-st order structure by taking predicates for analytic subsets of <jats:italic>X, X<\/jats:italic> x <jats:italic>X<\/jats:italic>, \u2026 as basic relations. Let <jats:italic>f<\/jats:italic>: <jats:italic>X<\/jats:italic> \u2192 <jats:italic>Y<\/jats:italic> be a <jats:italic>proper<\/jats:italic> surjective holomorphic map between complex spaces and set <jats:italic>X<jats:sub>y<\/jats:sub><\/jats:italic> \u2254 <jats:italic>f<\/jats:italic><jats:sup>\u22121<\/jats:sup>(<jats:italic>y<\/jats:italic>). We show that the set<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200008148_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>is analytically constructible, i.e.. is a <jats:italic>definable<\/jats:italic> set when <jats:italic>X<\/jats:italic> and <jats:italic>Y<\/jats:italic> are compact complex spaces and <jats:italic>f: X<\/jats:italic> \u2192 <jats:italic>Y<\/jats:italic> is a holomorphic map. The analogous result in the context of algebraic geometry gives rise to the definability of Morley degree.<\/jats:p>","DOI":"10.2178\/jsl\/1080938839","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:30:06Z","timestamp":1109799006000},"page":"241-254","source":"Crossref","is-referenced-by-count":3,"title":["A definability result for compact complex spaces"],"prefix":"10.1017","volume":"69","author":[{"given":"Dale","family":"Radin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200008148_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01425245"},{"key":"S0022481200008148_ref009","unstructured":"Moosa R. , Contributions to the model theory of fields and compact complex spaces, Ph.D. thesis , University of Illinois at Urbana-Champaign, 2001."},{"key":"S0022481200008148_ref010","first-page":"737","volume":"67","author":"Pillay","year":"2002","journal-title":"Compact complex manifolds with the DOP and other properties"},{"key":"S0022481200008148_ref002","first-page":"334","volume-title":"Bulletin des Sciences Math\u00e9matiques","author":"Cartan","year":"1933"},{"key":"S0022481200008148_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69582-7"},{"key":"S0022481200008148_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808211"},{"key":"S0022481200008148_ref001","volume-title":"Desingularization theorems","author":"Aroca","year":"1977"},{"key":"S0022481200008148_ref012","unstructured":"van den Dries L. , Model theory offields: decidability, and bounds for polynomial ideals, Ph.D. thesis , Universiteit Utrecht, 1978."},{"key":"S0022481200008148_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0080338"},{"key":"S0022481200008148_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7617-9"},{"key":"S0022481200008148_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01342886"},{"key":"S0022481200008148_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09873-8"},{"key":"S0022481200008148_ref013","volume-title":"Proceedings of the 10th Easter Conference on Model Theory","author":"Zilber","year":"1993"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200008148","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:28:10Z","timestamp":1557178090000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200008148\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["S0022481200008148"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1080938839","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}