Quasianalytic Denjoy-Carleman classes and o-minimality

Rolin, J.-P.; Speissegger, P.; Wilkie, A.

doi:10.1090/S0894-0347-03-00427-2

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.

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