Exponentially closed fields and the conjecture on intersections with tori

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Annals of Pure and Applied Logic 165 (11):1680-1706 (2014)
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Abstract

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

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10.1016/j.apal.2014.06.002

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Citations of this work

Model theory of special subvarieties and Schanuel-type conjectures.Boris Zilber - 2016 - Annals of Pure and Applied Logic 167 (10):1000-1028.
Adequate predimension inequalities in differential fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.

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References found in this work

Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.
Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.
On quasiminimal excellent classes.Jonathan Kirby - 2010 - Journal of Symbolic Logic 75 (2):551-564.
A Note on the Axioms for Zilber’s Pseudo-Exponential Fields.Jonathan Kirby - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):509-520.

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