Definably complete Baire structures

Antongiulio Fornasiero, and Tamara Servi. "Definably complete Baire structures." Fundamenta Mathematicae 209.3 (2010): 215-241. <http://eudml.org/doc/282678>.

@article{AntongiulioFornasiero2010,
abstract = {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.},
author = {Antongiulio Fornasiero, Tamara Servi},
journal = {Fundamenta Mathematicae},
keywords = {Pfaffian functions; definably complete structures; Baire spaces; o-minimality},
language = {eng},
number = {3},
pages = {215-241},
title = {Definably complete Baire structures},
url = {http://eudml.org/doc/282678},
volume = {209},
year = {2010},
}

TY - JOUR
AU - Antongiulio Fornasiero
AU - Tamara Servi
TI - Definably complete Baire structures
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 3
SP - 215
EP - 241
AB - 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.
LA - eng
KW - Pfaffian functions; definably complete structures; Baire spaces; o-minimality
UR - http://eudml.org/doc/282678
ER -