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Exponentially Closed Fields and the Conjecture on Intersections with Tori

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

preprint2014arXivOpen access
Jonathan KirbyBoris Zilber
math.LO
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Jonathan KirbyBoris Zilber

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