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A first-order version of Pfaffian closure

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Fratarcangeli S.

Fundamenta Mathematicae

2008

tom 198

nr 3

229-254

The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness theorem. We illustrate this advantage by deriving a uniformity result on the number of connected components for sets defined with Rolle leaves, the building blocks of Pfaffian-closed structures.

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1 Fundamenta Mathematicae

1 Fratarcangeli S.

1 2008

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A first-order version of Pfaffian closure