1 October 2010 The theorem of the complement for nested sub-Pfaffian sets
Jean-Marie Lion, Patrick Speissegger
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Duke Math. J. 155(1): 35-90 (1 October 2010). DOI: 10.1215/00127094-2010-050

Abstract

Let R be an o-minimal expansion of the real field, and let Lnest(R) be the language consisting of all nested Rolle leaves over R. We call a set nested sub-Pfaffian over R if it is the projection of a positive Boolean combination of definable sets and nested Rolle leaves over R. Assuming that R admits analytic cell decomposition, we prove that the complement of a nested sub-Pfaffian set over R is again a nested sub-Pfaffian set over R. As a corollary, we obtain that if R admits analytic cell decomposition, then the Pfaffian closure P(R) of R is obtained by adding to R all nested Rolle leaves over R, a one-stage process, and that P(R) is model complete in the language Lnest(R).

Citation

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Jean-Marie Lion. Patrick Speissegger. "The theorem of the complement for nested sub-Pfaffian sets." Duke Math. J. 155 (1) 35 - 90, 1 October 2010. https://doi.org/10.1215/00127094-2010-050

Information

Published: 1 October 2010
First available in Project Euclid: 23 September 2010

zbMATH: 1226.14075
MathSciNet: MR2730372
Digital Object Identifier: 10.1215/00127094-2010-050

Subjects:
Primary: 14P10 , 58A17
Secondary: 03C99

Rights: Copyright © 2010 Duke University Press

Vol.155 • No. 1 • 1 October 2010
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