University of Illinois Urbana-Champaign

The field of reals with Gevrey functions is model complete and o-minimal

Speissegger, Patrick Urs

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Description

Title
The field of reals with Gevrey functions is model complete and o-minimal
Author(s)
Speissegger, Patrick Urs
Issue Date
1996
Doctoral Committee Chair(s)
van den Dries, Lou
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
  • Infinitely representable functions are introduced, and it is proved that the expansion $\IR\sb{\cal G}$ of the field of reals by a certain subfamily of all infinitely representable functions (namely, the family of so-called Gevrey functions) is model complete and o-minimal as well as polynomially bounded. The function $\phi$ given on (1, $\infty$) by$$\log\Gamma(x)=\left(x-{1\over2}\right)\log x-x+{1\over2}\log(2\pi)+\phi(x)$$is definable in $\IR\sb{\cal G},$ as are all functions whose Taylor series expansion at the origin is multisummable in the direction $\IR\sp+$.
  • The class of all infinitely representable functions is shown to be the same as the class of all finite sums of functions satisfying Gevrey estimates on disks (rather than on sectors of large enough opening). This leads to a generalization of the theory of multisummability in the direction $\IR\sp+$. An example of an infinitely representable function whose Taylor series is not multisummable in the direction $\IR\sp+$ is constructed.
Type of Resource
text
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http://hdl.handle.net/2142/22842
Copyright and License Information
Copyright 1996 Speissegger, Patrick Urs

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