Definably complete Baire structures
Definably complete Baire structures
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绝对完整的贝尔结构
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Tamara Servi
中科院分区：
文献类型：
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作者：
A. Fornasiero;Tamara Servi
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.
