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Diophantine properties of sets definable in o-minimal structures
Published online by Cambridge University Press: 12 March 2014
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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]).
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- Copyright © Association for Symbolic Logic 2004
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