{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:25Z","timestamp":1753880845588,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"the ERC project TOSSIBERG","award":["637027"],"award-info":[{"award-number":["637027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2022,8,1]]},"abstract":"<jats:p> We show that every definable nested family of closed and bounded subsets of a P-minimal field K has nonempty intersection. As an application we answer a question of Darni\u00e8re and Halupczok showing that P-minimal fields satisfy the \u201cextreme value property\u201d: for every closed and bounded subset [Formula: see text] and every interpretable continuous function [Formula: see text] (where [Formula: see text] denotes the value group), f(U) admits a maximal value. Two further corollaries are obtained as a consequence of their work. The first one shows that every interpretable subset of [Formula: see text] is already interpretable in the language of rings, answering a question of Cluckers and Halupczok. This implies in particular that every P-minimal field is polynomially bounded. The second one characterizes those P-minimal fields satisfying a classical cell preparation theorem as those having definable Skolem functions, generalizing a result of Mourgues. <\/jats:p>","DOI":"10.1142\/s0219061322500040","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T09:27:13Z","timestamp":1655890033000},"source":"Crossref","is-referenced-by-count":0,"title":["Definable completeness of <i>P<\/i>-minimal fields and applications"],"prefix":"10.1142","volume":"22","author":[{"given":"Pablo","family":"Cubides Kovacsics","sequence":"first","affiliation":[{"name":"Mathematisches Institut der Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstr. 1, 40225 D\u00fcsseldorf, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7oise","family":"Delon","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Paris and Sorbonne Universit\u00e9, CNRS, Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche, F-75006 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"S0219061322500040BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2017.06.002"},{"key":"S0219061322500040BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061320500051"},{"key":"S0219061322500040BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-03-03458-5"},{"key":"S0219061322500040BIB004","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1045861509"},{"key":"S0219061322500040BIB005","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1333566641"},{"key":"S0219061322500040BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2015.79"},{"issue":"3","key":"S0219061322500040BIB007","first-page":"413","volume":"21","author":"Delon F.","year":"2012","journal-title":"Ann. Fac. Sci. Toulouse Math."},{"key":"S0219061322500040BIB008","first-page":"154","volume":"369","author":"Denef J.","year":"1986","journal-title":"J. Reine Angew. Math."},{"key":"S0219061322500040BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-020-1992-1"},{"key":"S0219061322500040BIB010","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2015.38"},{"key":"S0219061322500040BIB011","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2016.58"},{"key":"S0219061322500040BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1195484-5"},{"key":"S0219061322500040BIB013","doi-asserted-by":"publisher","DOI":"10.2307\/2694974"},{"key":"S0219061322500040BIB014","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200810009"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061322500040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T04:07:00Z","timestamp":1665374820000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061322500040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,22]]},"references-count":14,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2022,8,1]]}},"alternative-id":["10.1142\/S0219061322500040"],"URL":"https:\/\/doi.org\/10.1142\/s0219061322500040","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2022,6,22]]},"article-number":"2250004"}}