Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2004, June 14.

Abstract:
Modifying the proof of a theorem of Wilkie, it is shown that if a one dimnsional set $S$ is definable in an O-minimal expansion of the ordered field of the reals, and if it is regularly exponentially near to many integral points, then there is an unbounded set, which is ${\cal R}$ definable without parameters, and which is exponentially near to $S$.

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