HomePublications

Exponentially Closed Fields and the Conjecture on Intersections with Tori

Research output: Contribution to journalArticle

Standard

Exponentially Closed Fields and the Conjecture on Intersections with Tori. / Kirby, Jonathan; Zilber, Boris.

In: Annals of Pure and Applied Logic, Vol. 165, No. 11, 11.2014, p. 1680-1706.

Research output: Contribution to journalArticle

Harvard

APA

Vancouver

Author

Bibtex- Download

@article{97a8d03ef73c4aae958c220d3ccde1bf,
title = "Exponentially Closed Fields and the Conjecture on Intersections with Tori",
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.",
keywords = "math.LO, 03C65, 11G35, Exponential fields, Anomalous intersections, Schanuel's conjecture, Predimension",
author = "Jonathan Kirby and Boris Zilber",
year = "2014",
month = nov,
doi = "10.1016/j.apal.2014.06.002",
language = "English",
volume = "165",
pages = "1680--1706",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier",
number = "11",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Exponentially Closed Fields and the Conjecture on Intersections with Tori

AU - Kirby, Jonathan

AU - Zilber, Boris

PY - 2014/11

Y1 - 2014/11

N2 - 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.

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

U2 - 10.1016/j.apal.2014.06.002

DO - 10.1016/j.apal.2014.06.002

M3 - Article

VL - 165

SP - 1680

EP - 1706

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 11

ER -

ID: 38608462