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Autorzy
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Języki publikacji
Abstrakty
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable increasing family of nowhere dense sets. Every expansion of the real field is definably complete and Baire, and so is every o-minimal expansion of a field. Moreover, unlike the o-minimal case, the structures considered form an axiomatizable class. In this context we prove a version of the Kuratowski-Ulam Theorem, some restricted version of Sard's Lemma and a version of Khovanskii's Finiteness Theorem. We apply these results to prove the o-minimality of every definably complete Baire expansion of an ordered field with any family of definable Pfaffian functions.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
215-241
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Institut für Mathematische Logik, Einsteinstr. 62, 48149 Münster, Germany
autor
- Centro de Matemática, e Aplicações Fundamentais, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-2