Exponentially closed fields and the conjecture on intersections with tori

Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107 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, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	26 Nov 2014 14:26
Last Modified:	07 Nov 2024 12:38
URI:	https://ueaeprints.uea.ac.uk/id/eprint/50700
DOI:	10.1016/j.apal.2014.06.002

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