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Quasianalytic Denjoy-Carleman classes and o-minimality

Authors: J.-P. Rolin, P. Speissegger and A. J. Wilkie
Journal: J. Amer. Math. Soc. 16 (2003), 751-777
MSC (2000): Primary 14P15, 03C64; Secondary 32S45
Published electronically: March 21, 2003
MathSciNet review: 1992825
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Abstract: We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure conditions. Some of these structures do not admit analytic cell decomposition, and they show that there is no largest o-minimal expansion of the real field.

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Additional Information

J.-P. Rolin
Affiliation: Laboratoire de Topologie, Université de Bourgogne, 9 Av. Alain Savary, B.P. 47870, 21078 Dijon Cedex, France

P. Speissegger
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706

A. J. Wilkie
Affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford OX1 3LB, United Kingdom

Keywords: Quasianalytic classes, o-minimal structures, resolution of singularities
Received by editor(s): February 19, 2001
Published electronically: March 21, 2003
Additional Notes: Supported in part by CNRS, NSERC grant OGP0009070 and NSF grant DMS-9988453
Article copyright: © Copyright 2003 American Mathematical Society