{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T11:25:58Z","timestamp":1751887558817},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":501,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the<jats:italic>p<\/jats:italic>-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories of valued fields.<\/jats:p>","DOI":"10.2178\/bsl\/1344861887","type":"journal-article","created":{"date-parts":[[2012,8,13]],"date-time":"2012-08-13T12:44:52Z","timestamp":1344861892000},"page":"368-381","source":"Crossref","is-referenced-by-count":1,"title":["Model Theory of Analytic Functions: Some Historical Comments"],"prefix":"10.1017","volume":"18","author":[{"given":"Deirdre","family":"Haskell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600000020_ref023","first-page":"441","volume-title":"Kreiseliana","author":"Macintyre","year":"1996"},{"key":"S1079898600000020_ref005","doi-asserted-by":"crossref","first-page":"141","DOI":"10.4171\/dms\/1-2\/13","article-title":"p-adic analytic spaces","volume":"II","author":"Berkovich","year":"1998","journal-title":"Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)"},{"key":"S1079898600000020_ref030","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/033"},{"key":"S1079898600000020_ref033","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1951-0041081-0"},{"key":"S1079898600000020_ref011","first-page":"18","article-title":"Projections of semianalytic sets","volume":"2","author":"GabrieLov","year":"1968","journal-title":"Akademija Nauk SSSR. Funkcional'nyi Analiz i ego Prilo\u017eenija"},{"key":"S1079898600000020_ref015","unstructured":"Hrushovski E. and Loeser F. , Non-archimedean tame topology and stably dominated types, arXiv:1009.0252."},{"key":"S1079898600000020_ref010","first-page":"5","volume-title":"Algebra i Logika Sem. 4","author":"Ersov","year":"1965"},{"key":"S1079898600000020_ref007","first-page":"37","volume-title":"Contributions to algebra (collection of papers dedicated to Ellis Kolchin)","author":"Blum","year":"1977"},{"key":"S1079898600000020_ref036","doi-asserted-by":"crossref","DOI":"10.1525\/9780520348097","volume-title":"A decision methodfor elementary algebra and geometry","author":"Tarski","year":"1951"},{"key":"S1079898600000020_ref045","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.07.001"},{"key":"S1079898600000020_ref026","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.05.014"},{"key":"S1079898600000020_ref021","volume-title":"Ensembles semi-analytiques","author":"\u0141ojasiewicz","year":"1965"},{"key":"S1079898600000020_ref002","first-page":"846","article-title":"On the undecidability of power series fields","volume":"16","author":"Ax","year":"1965","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S1079898600000020_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/1970774"},{"key":"S1079898600000020_ref019","volume-title":"Introduction to transcendental numbers","author":"Lang","year":"1966"},{"key":"S1079898600000020_ref028","first-page":"230","article-title":"Model theory and complex geometry","volume":"57","author":"Moosa","year":"2010","journal-title":"Notices of the American Mathematical Society"},{"key":"S1079898600000020_ref034","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-03-00427-2"},{"key":"S1079898600000020_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1971463"},{"key":"S1079898600000020_ref025","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1154698577"},{"key":"S1079898600000020_ref040","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00216-0"},{"key":"S1079898600000020_ref044","first-page":"202","volume-title":"Seminarberichte Nr 93-1, Proceedings of the 10th Easter Conference in Model Theory, April 12\u201317, 1993","author":"Zilber","year":"1993"},{"key":"S1079898600000020_ref008","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160220202"},{"key":"S1079898600000020_ref014","first-page":"453","volume-title":"Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki","author":"Hironaka","year":"1973"},{"key":"S1079898600000020_ref029","doi-asserted-by":"publisher","DOI":"10.1007\/PL00001405"},{"key":"S1079898600000020_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/1970476"},{"key":"S1079898600000020_ref024","first-page":"753","article-title":"Model theory and exponentiation","volume":"43","author":"Marker","year":"1996","journal-title":"Notices of the American Mathematical Society"},{"key":"S1079898600000020_ref038","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1986-15468-6"},{"key":"S1079898600000020_ref039","volume-title":"Model theory, algebra and geometry","author":"van den Dries","year":"2000"},{"key":"S1079898600000020_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02699126"},{"key":"S1079898600000020_ref037","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71811-1"},{"key":"S1079898600000020_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01436073"},{"key":"S1079898600000020_ref041","volume-title":"Models and Computability, Proceedings of Logic Colloquium 1997","author":"Wilkie","year":"1997"},{"key":"S1079898600000020_ref032","first-page":"427","volume-title":"Theory of sets and topology (in honour of Felix Hausdorff, 1868\u20131942)","author":"Robinson","year":"1972"},{"key":"S1079898600000020_ref001","unstructured":"Aschenbrenner M. , Review of [45]. mr2102856, 2006."},{"key":"S1079898600000020_ref013","first-page":"175","article-title":"Definable sets in algebraically closed valued fields: elimination of imaginaries","volume":"597","author":"Haskell","year":"2006","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"key":"S1079898600000020_ref043","first-page":"383","volume-title":"Logic colloquium 2000","author":"Wilkie","year":"2005"},{"key":"S1079898600000020_ref035","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1999.508.189"},{"key":"S1079898600000020_ref022","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200051173"},{"key":"S1079898600000020_ref042","doi-asserted-by":"publisher","DOI":"10.1007\/s000290050052"},{"key":"S1079898600000020_ref016","unstructured":"Hrushovski E. and Martin B. , Zeta functions from definable equivalence relations, arXiv:math\/0701011."},{"key":"S1079898600000020_ref027","volume":"20","author":"Moosa","year":"2005"},{"key":"S1079898600000020_ref020","doi-asserted-by":"publisher","DOI":"10.2307\/2374723"},{"key":"S1079898600000020_ref017","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0833698-1"},{"key":"S1079898600000020_ref018","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1052669055"},{"key":"S1079898600000020_ref031","first-page":"113","volume-title":"Bulletin of the Research Council of Israel Section F","author":"Robinson","year":"1959"}],"container-title":["The Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600000020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T09:00:25Z","timestamp":1687683625000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600000020\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S1079898600000020"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1344861887","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}