Illinois Journal of Mathematics

Relative Pfaffian closure for definably complete Baire structures

Antongiulio Fornasiero and Tamara Servi

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Speissegger proved that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Here we give a first order version of this result: having introduced the notion of definably complete Baire structure, we define the relative Pfaffian closure of an o-minimal structure inside a definably complete Baire structure, and we prove its o-minimality. We derive effective bounds on some topological invariants of sets definable in the Pfaffian closure of an o-minimal expansion of the real field.

Article information

Illinois J. Math., Volume 55, Number 3 (2011), 1203-1219.

First available in Project Euclid: 29 May 2013

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Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 58A17: Pfaffian systems 32C05: Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07] 54E52: Baire category, Baire spaces 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]


Fornasiero, Antongiulio; Servi, Tamara. Relative Pfaffian closure for definably complete Baire structures. Illinois J. Math. 55 (2011), no. 3, 1203--1219. doi:10.1215/ijm/1369841803.

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