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THE FIELD OF REALS WITH MULTISUMMABLE SERIES AND THE EXPONENTIAL FUNCTION

Published online by Cambridge University Press:  03 November 2000

LOU VAN DEN DRIES  and
PATRICK SPEISSEGGER
LOU VAN DEN DRIES
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA, [email protected]
PATRICK SPEISSEGGER
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA, [email protected]
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Abstract

We show that the field of real numbers with multisummable real power series is model complete, o-minimal and polynomially bounded. Further expansion by the exponential function yields again a model complete and o-minimal structure which is exponentially bounded, and in which the Gamma function on the positive real line is definable. 2000 Mathematics Subject Classification: primary 03C10, 32B05, 32B20; secondary, 26E05.

Keywords

o-minimal structuresmodel completenesspower seriesblowing-up
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 81 , Issue 3 , November 2000 , pp. 513 - 565
Copyright
2000 London Mathematical Society

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