We develop a variation of the Pila-Wilkie counting theorem, where we count rational points that approximate bounded complex analytic sets. A unique aspect of our result is that it does not depend on the analytic set (or family) in question. We apply this approximate counting to obtain an effective Pila-Wilkie type statement for analytic sets cut out by computable functions.
This is joint work with Gal Binyamini | 
