The rational points of a definable set

J. Pila; A. J. Wilkie

doi:10.1215/S0012-7094-06-13336-7

15 June 2006 The rational points of a definable set

J. Pila, A. J. Wilkie

Author Affiliations +

Abstract

Let $X\subset\mathbb{R}^n$ be a set that is definable in an o-minimal structure over ${\mathbb R}$ . 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

Citation Download Citation

J. Pila and A. J. Wilkie "The rational points of a definable set," Duke Mathematical Journal 133(3), 591-616, (15 June 2006). https://doi.org/10.1215/S0012-7094-06-13336-7

Published: 15 June 2006

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS