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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
Email: rolin@u-bourgogne.fr

P. Speissegger
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: speisseg@math.wisc.edu

A. J. Wilkie
Affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford OX1 3LB, United Kingdom
Email: wilkie@maths.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S0894-0347-03-00427-2
PII: S 0894-0347(03)00427-2
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