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Uniform bounds on growth in o-minimal structures

✍ Scribed by Janak Ramakrishnan

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 73 KB
Volume: 56
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200910031

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✦ Synopsis

Abstract

We prove that a function definable with parameters in an o‐minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in [1]. Moreover, this remains true if the argument is taken to approach any element of the structure (or ±∞), and the function has limit any element of the structure (or ±∞) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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