On the Main Lemma in the Pila-Wilkie counting theorem (after Bombieri, Pila and Wilkie)  

Khoa Dang Nguyen1 

1Department of Mathematics, The University of British Columbia, Vancouver, BC V6T 1Z2, Canada

* To whom correspondence should be addressed: dknguyen@math.ubc.ca

 Abstract

 In this short article, we review the Pila-Wilkie counting theorem which plays a crucial role in Pila’s recent results on the André-Oort conjecture. In fact, we will focus on the so-called Main Lemma in many of Pila’s papers. 

Keywords: Bombieri-Pila theorem, Pila-Wilkie counting theorem, o-minimality

Publicaton Date (Web): May 25, 2016
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Editor: Thanh Vu, University of Nebraska-Lincoln, USA