Counting special points: logic, Diophantine geometry, and transcendence theory
T Scanlon - Bulletin of the American Mathematical Society, 2012 - ams.org
Bulletin of the American Mathematical Society, 2012•ams.org
… We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal
structures and some applications of this theorem to problems in diophantine geometry due to
Masser, Peterzil, Pila, Starchenko, and Zannier. … Over the past decade and a half, starting
with Hrushovski’s proof of the function field Mordell-Lang conjecture [12], some of the more
refined theorems from model theory in the sense of mathematical logic have been applied to
problems in diophantine geometry. In most of these cases, the technical results underlying the …
structures and some applications of this theorem to problems in diophantine geometry due to
Masser, Peterzil, Pila, Starchenko, and Zannier. … Over the past decade and a half, starting
with Hrushovski’s proof of the function field Mordell-Lang conjecture [12], some of the more
refined theorems from model theory in the sense of mathematical logic have been applied to
problems in diophantine geometry. In most of these cases, the technical results underlying the …
Abstract
We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier. References
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