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Definably complete Baire structures

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Fornasiero A., Servi T.

Fundamenta Mathematicae

2010

tom 209

nr 3

215-241

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Fornasiero A.

1 Servi T.

1 2010

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Definably complete Baire structures