Exponentially closed fields and the conjecture on intersections with tori

Kirby, Jonathan and Zilber, Boris (2014) Exponentially closed fields and the conjecture on intersections with tori. Annals of Pure and Applied Logic, 165 (11). pp. 1680-1706. ISSN 0168-0072

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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.

Item Type:	Article
Uncontrolled Keywords:	math.lo,03c65, 11g35,exponential fields,anomalous intersections,schanuel's conjecture,predimension
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Pure Connector
Date Deposited:	26 Nov 2014 14:26
Last Modified:	15 Jul 2025 08:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/50700
DOI:	10.1016/j.apal.2014.06.002

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