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Diophantine properties of sets definable in o-minimal structures

Published online by Cambridge University Press:  12 March 2014

A. J. Wilkie
A. J. Wilkie*
Affiliation:
Mathematical Institute, 24-29 ST Giles, Oxford OX1 3LB, UK, E-mail: wilkie@maths.ox.ac.uk
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Extract

Let be an o-minimal expansion of the ordered field of real numbers , and let S be an -definable subset (parameters allowed unless otherwise stated) of ℝn. In this note I investigate questions concerning the distribution of points on S with integer coordinates. My main theorem gives an estimate which, though probably far from best possible, at least shows that the o-minimal assumption does have diophantine consequences. This is, perhaps, surprising in view of the flexibility that we now seem to have in constructing o-minimal expansions of (see, e. g. [7], [8], [9]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 851 - 861
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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