Seminários de Lógica Matemática

27 de Novembro 2008, 18h00

Definably complete and Baire structures: a first order approach to real geometry. (Joint work with A. Fornasiero)
Complexo Interdisciplinar, Sala B3-01

TAMARA SERVI (CMAF - Universidade de Lisboa)

Abstract:

I will give a survey of the topic: motivation for the study of these structures, definitions, main properties, applications. We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not 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. So is every o-minimal expansion of a field. The converse is clearly not true. However, unlike the o-minimal case, the structures considered form an elementary class. We prove the o-minimality of every definably complete and Baire expansion of an ordered field with any family of definable Pfaffian functions. We apply this result to obtain a simple candidate for a recursive axiomatization of the theory of the real exponential field, and some related structures.

[At the end of the talk we will decide together which aspects will be further discussed in the Model Theory Seminar.]

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