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University of Illinois at Urbana-Champaign
The field of reals with Gevrey functions is model complete and o-minimal
Abstract
dc:descriptionInfinitely 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$\log\Gamma(x)=\left(x-{1\over2}\right)\log x-x+{1\over2}\log(2π)+\phi(x)$is definable in $\IR\sb{\cal G},$ as are all functions whose Taylor series expansion at the origin is multisummable in the direction $\IR\sp+$.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Speissegger, Patrick Urs
- Contributors dc:contributor
-
- van den Dries, Lou
Subjects
dc:subject × 1Rights
dc:rights- Statement dc:rights
-
- Copyright 1996 Speissegger, Patrick Urs
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
-
9780591200003
AAI9712443
(UMI)AAI9712443 - OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/22842