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2012.4: Locally polynomially bounded structures

2012.4: A J Wilkie and G O Jones (2008) Locally polynomially bounded structures. Bulletin of the London Mathematical Society, 40 (2). pp. 239-248.

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DOI: 10.1112/blms/bdn004

Abstract

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 2000 > 03 Mathematical logic and foundations
MSC 2000 > 26 Real functions
MIMS number:2012.4
Deposited By:Prof Alex J Wilkie
Deposited On:05 January 2012

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