Definably complete Baire structures

• Autorzy: Antongiulio Fornasiero , Tamara Servi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 58A17: Pfaffian systems
• 32C05: Real-analytic manifolds, real-analytic spaces
• 03C64: Model theory of ordered structures; o-minimality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 3
• Strony: 215-241

Daty

wydano

2010

Twórcy

autor

Antongiulio Fornasiero

• Institut für Mathematische Logik, Einsteinstr. 62, 48149 Münster, Germany

autor

Tamara Servi

• Centro de Matemática, e Aplicações Fundamentais, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Identyfikatory

DOI

10.4064/fm209-3-2