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2007.198: The rational points of a definable set

2007.198: J. Pila and A. J. Wilkie (2006) The rational points of a definable set. Duke Mathematical Journal, 133 (3). pp. 591-616. ISSN 0012-7094

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

Abstract

Let $X\R^n$ 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

Item Type:Article
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 11 Number theory
MIMS number:2007.198
Deposited By:Mrs Louise Healey
Deposited On:21 November 2007

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