Duke Mathematical Journal

The rational points of a definable set

J. Pila and A. J. Wilkie

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Let XRn be a set that is definable in an o-minimal structure over R. This article shows that in a suitable sense, there are very few rational points of X which do not lie on some connected semialgebraic subset of X of positive dimension

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Duke Math. J., Volume 133, Number 3 (2006), 591-616.

First available in Project Euclid: 13 June 2006

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Zentralblatt MATH identifier

Primary: 11G99: None of the above, but in this section 03C64: Model theory of ordered structures; o-minimality


Pila, J.; Wilkie, A. J. The rational points of a definable set. Duke Math. J. 133 (2006), no. 3, 591--616. doi:10.1215/S0012-7094-06-13336-7. https://projecteuclid.org/euclid.dmj/1150201203

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