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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Quasianalytic Denjoy-Carleman classes and o-minimality
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by J.-P. Rolin, P. Speissegger and A. J. Wilkie PDF
J. Amer. Math. Soc. 16 (2003), 751-777 Request permission

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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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
  • 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