Exponentially closed fields and the conjecture on intersections with tori

Jonathan Kirby; Boris Zilber

doi:10.1016/j.apal.2014.06.002

Exponentially closed fields and the conjecture on intersections with tori

Jonathan Kirby, Boris Zilber

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	1680-1706
Number of pages	27
Journal	Annals of Pure and Applied Logic
Volume	165
Issue number	11
Early online date	9 Jul 2014
DOIs	https://doi.org/10.1016/j.apal.2014.06.002
Publication status	Published - Nov 2014

Keywords

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

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10.1016/j.apal.2014.06.002

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Jonathan Kirby
- Jonathan.Kirbyuea.acuk
- School of Engineering, Mathematics and Physics - Reader
- Algebra, Number Theory, Logic, and Representations (ANTLR) - Member
Person: Research Group Member, Academic, Teaching and Research

Cite this

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AB - 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.

KW - math.LO

KW - 03C65, 11G35

KW - Exponential fields

KW - Anomalous intersections

KW - Schanuel's conjecture

KW - Predimension

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DO - 10.1016/j.apal.2014.06.002

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Exponentially closed fields and the conjecture on intersections with tori

Abstract

Keywords

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Jonathan Kirby

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