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Locally Polynomially Bounded Structures

G. O. Jones·A. J. Wilkie
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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 language.

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BibTeXRIS

G. O. Jones, A. J. Wilkie. 2007-01-22. Locally Polynomially Bounded Structures. https://doi.org/10.1112/blms%2Fbdn004

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