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Pfaffian Sets and O-minimality

  • Patrick Speissegger
Chapter
Part of the Fields Institute Communications book series (FIC, volume 62)

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 

Notes

Acknowledgements

Supported by the Fields Institute for Research in the Mathematical Sciences and by NSERC of Canada grant RGPIN 261961.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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