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

 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