Exponentially closed fields and the conjecture on intersections with tori

&
Annals of Pure and Applied Logic 165 (11):1680-1706 (2014)
  Copy   BIBTEX

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

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2014.06.002

Other Versions

No versions found

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A Note on the Axioms for Zilber’s Pseudo-Exponential Fields.Jonathan Kirby - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):509-520.
Real Closed Exponential Subfields of Pseudo-Exponential Fields.Ahuva C. Shkop - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):591-601.
Elementary geometric local–global principles for fields.Arno Fehm - 2013 - Annals of Pure and Applied Logic 164 (10):989-1008.
Raising to powers in algebraically closed fields.B. Zilber - 2003 - Journal of Mathematical Logic 3 (02):217-238.
Pseudo real closed fields, pseudo p-adically closed fields and NTP2.Samaria Montenegro - 2017 - Annals of Pure and Applied Logic 168 (1):191-232.
Computable categoricity for pseudo-exponential fields of size ℵ 1.Jesse Johnson - 2014 - Annals of Pure and Applied Logic 165 (7-8):1301-1317.
Pseudo-exponentiation on algebraically closed fields of characteristic zero.Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.
Intersections of algebraically closed fields.C. J. Ash & John W. Rosenthal - 1986 - Annals of Pure and Applied Logic 30 (2):103-119.
A consistency proof for elementary algebra and geometry.Harvey Friedman - manuscript
Adequate predimension inequalities in differential fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.

Analytics

Added to PP
2015-01-22

Downloads
55 (#1,088,247)

6 months
3 (#1,865,063)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Model theory of special subvarieties and Schanuel-type conjectures.Boris Zilber - 2016 - Annals of Pure and Applied Logic 167 (10):1000-1028.
Generic multiplicative endomorphism of a field.Christian D'Elbée - 2025 - Annals of Pure and Applied Logic 176 (4):103554.
Adequate predimension inequalities in differential fields.Vahagn Aslanyan - 2022 - Annals of Pure and Applied Logic 173 (1):103030.

Add more citations

References found in this work

Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.
On quasiminimal excellent classes.Jonathan Kirby - 2010 - Journal of Symbolic Logic 75 (2):551-564.
A Note on the Axioms for Zilber’s Pseudo-Exponential Fields.Jonathan Kirby - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):509-520.

View all 7 references / Add more references