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Exponentially Closed Fields and the Conjecture on Intersections with Tori

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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.

Details

Original languageEnglish
Pages (from-to)1680-1706
Number of pages27
JournalAnnals of Pure and Applied Logic
Volume165
Issue number11
Early online date9 Jul 2014
DOIs
Publication statusPublished - Nov 2014
Peer-reviewedYes

Keywords

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  • math.LO, 03C65, 11G35, Exponential fields, Anomalous intersections, Schanuel's conjecture, Predimension

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