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We give an axiomatization of the class ECF of exponentially closed fields,which includes the pseudo-exponential fields previously introduced by thesecond author, and show that it is superstable over its interpretation ofarithmetic. Furthermore, ECF is exactly the elementary class of thepseudo-exponential fields if and only if the diophantine conjecture CIT onatypical intersections of tori with subvarieties is true.

Exponentially Closed Fields and the Conjecture on Intersections with Tori