A first-order version of Pfaffian closure

Volume 198 / 2008

Sergio Fratarcangeli Fundamenta Mathematicae 198 (2008), 229-254 MSC: Primary 03C64; Secondary 58A17. DOI: 10.4064/fm198-3-3


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.


  • Sergio FratarcangeliDivision of Natural Sciences and Mathematics
    The College of New Rochelle
    29 Castle Place
    New Rochelle, NY 10805, U.S.A.

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