A first-order version of Pfaffian closure

• Autorzy: Sergio Fratarcangeli
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58A17: Pfaffian systems
• 03C64: Model theory of ordered structures; o-minimality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 198
• Numer: 3
• Strony: 229-254

Daty

wydano

2008

Twórcy

autor

Sergio Fratarcangeli

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

Identyfikatory

DOI

10.4064/fm198-3-3