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.
Mathematics Subject Classification (2010): Primary 14P15, 58A17, Secondary 03C64
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Supported by the Fields Institute for Research in the Mathematical Sciences and by NSERC of Canada grant RGPIN 261961.
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Speissegger, P. (2012). Pfaffian Sets and O-minimality. In: Miller, C., Rolin, JP., Speissegger, P. (eds) Lecture Notes on O-Minimal Structures and Real Analytic Geometry. Fields Institute Communications, vol 62. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4042-0_5
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