Notre Dame Journal of Formal Logic

Mildness and the Density of Rational Points on Certain Transcendental Curves

G. O. Jones, D. J. Miller, and M. E. M. Thomas


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.

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Notre Dame J. Formal Logic, Volume 52, Number 1 (2011), 67-74.

First available in Project Euclid: 13 December 2010

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Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality 11G99: None of the above, but in this section 11U09: Model theory [See also 03Cxx]

Pfaffian functions parameterization rational points


Jones, G. O.; Miller, D. J.; Thomas, M. E. M. Mildness and the Density of Rational Points on Certain Transcendental Curves. Notre Dame J. Formal Logic 52 (2011), no. 1, 67--74. doi:10.1215/00294527-2010-037.

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