Locally polynomially bounded structures

Wilkie, A J and Jones, G O (2008) Locally polynomially bounded structures. Bulletin of the London Mathematical Society, 40 (2). pp. 239-248.

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We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed o-minimal and polynomially bounded reduct. As an application we show that in certain o-minimal structures definable functions are piecewise implicitly defined over the basic functions in the in the language.

Item Type: Article
Uncontrolled Keywords: O-minimality
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 26 Real functions
Depositing User: Prof Alex J Wilkie
Date Deposited: 05 Jan 2012
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1744

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