Locally Polynomially Bounded Structures
Logic
2014-02-26 v2
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.
Cite
@article{arxiv.math/0701523,
title = {Locally Polynomially Bounded Structures},
author = {G. O. Jones and A. J. Wilkie},
journal= {arXiv preprint arXiv:math/0701523},
year = {2014}
}
Comments
Change of title