Mildness and the density of rational points on certain transcendental curves

Jones, G. O. and Miller, D. J. and Thomas, M. E. M. (2011) Mildness and the density of rational points on certain transcendental curves. Notre Dame Journal of Formal Logic, 52 (1). pp. 67-74.

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Official URL: http://projecteuclid.org/euclid.ndjfl/1292249611

Abstract

We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions.

Item Type: Article
Additional Information: This is an updated version of the preprint. It differs slightly from the published version.
Uncontrolled Keywords: Pfaffian functions; parameterization; rational points
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
Depositing User: Gareth Jones
Date Deposited: 17 May 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2135

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