A first-order version of Pfaffian closure

Sergio Fratarcangeli. "A first-order version of Pfaffian closure." Fundamenta Mathematicae 198.3 (2008): 229-254. <http://eudml.org/doc/282924>.

@article{SergioFratarcangeli2008,
abstract = {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.},
author = {Sergio Fratarcangeli},
journal = {Fundamenta Mathematicae},
keywords = {Pfaffian closure; o-minimal structures},
language = {eng},
number = {3},
pages = {229-254},
title = {A first-order version of Pfaffian closure},
url = {http://eudml.org/doc/282924},
volume = {198},
year = {2008},
}

TY - JOUR
AU - Sergio Fratarcangeli
TI - A first-order version of Pfaffian closure
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 3
SP - 229
EP - 254
AB - 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.
LA - eng
KW - Pfaffian closure; o-minimal structures
UR - http://eudml.org/doc/282924
ER -