Submission date: 4 August 2011.

Abstract:

We give an axiomatization of a class of exponential fields including the pseudo-exponential fields previously introduced by the second author, which is tame (superstable) over its interpretation of arithmetic. This class is exactly the elementary class of pseudo-exponential fields if and only if the diophantine conjecture CIT on atypical intersections of tori with subvarieties is true.

Mathematics Subject Classification: 03C65, 11G35

Keywords and phrases:

Full text arXiv 1108.1075: pdf, ps.