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Lecture Notes on O-Minimal Structures and Real Analytic Geometry

Volume 62 of the series Fields Institute Communications pp 179-218

Date:

Pfaffian Sets and O-minimality

  • Patrick SpeisseggerAffiliated withDepartment of Mathematics and Statistics, McMaster University Email author 

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Abstract

Recent developments in the theory of pfaffian sets are presented from a model-theoretic point of view. In particular, the current state of affairs for Van den Dries’s model-completeness conjecture is discussed in some detail. I prove the o-minimality of the pfaffian closure of an o-minimal structure, and I extend a weak model completeness result, originally proved as Theorem 5.1 in (J.-M. Lion and P. Speissegger, Duke Math J 103:215–231, 2000), to certain reducts of the pfaffian closure, such as the reduct generated by a single pfaffian chain.

Keywords

Pfaffian functions O-minimal structures Model completeness