Submission date: 18 April 2013.

Abstract:

We show that a natural, two sorted L_{\omega_1,\omega} theory involving the modular j-function is categorical in all uncountable cardinalities. It is also shown that a slight weakening of the adelic Mumford-Tate conjecture for products of elliptic curves is necessary and (along with a couple of other results from arithmetic geometry) sufficient for categoricity.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1304.4787: pdf, ps.