Quasianalytic Denjoy-Carleman classes and o-minimality
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- by J.-P. Rolin, P. Speissegger and A. J. Wilkie
- J. Amer. Math. Soc. 16 (2003), 751-777
- DOI: https://doi.org/10.1090/S0894-0347-03-00427-2
- Published electronically: March 21, 2003
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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.References
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Bibliographic 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
- MR Author ID: 361060
- 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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: J. Amer. Math. Soc. 16 (2003), 751-777
- MSC (2000): Primary 14P15, 03C64; Secondary 32S45
- DOI: https://doi.org/10.1090/S0894-0347-03-00427-2
- MathSciNet review: 1992825