Exponentially closed fields and the conjecture on intersections with tori

DOI10.1016/j.apal.2014.06.002zbMath1315.03056arXiv1108.1075OpenAlexW2034904171WikidataQ123299947 ScholiaQ123299947MaRDI QIDQ400418

Jonathan Kirby, B. I. Zil'ber

Publication date: 21 August 2014

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.1075

zbMATH Keywords

exponential fieldsSchanuel's conjectureanomalous intersectionspredimension

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45) Model theory (number-theoretic aspects) (11U09) Categoricity and completeness of theories (03C35)

Related Items (11)

Model theory of special subvarieties and Schanuel-type conjectures ⋮ Pseudo-exponential maps, variants, and quasiminimality ⋮ Weak modular Zilber-Pink with derivatives ⋮ A note on the axioms for Zilber's pseudo-exponential fields ⋮ Mini-workshop: Topological and differential expansions of o-minimal structures. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ Independence relations for exponential fields ⋮ Adequate predimension inequalities in differential fields ⋮ Blurred complex exponentiation ⋮ Forcing the truth of a weak form of Schanuel's conjecture ⋮ Solutions of equations involving the modular 𝑗 function ⋮ Tropical varieties for exponential sums

Cites Work

• Unnamed Item
• Unnamed Item
• Finitely presented exponential fields
• A note on the axioms for Zilber's pseudo-exponential fields
• Pseudo-exponentiation on algebraically closed fields of characteristic zero
• The theory of the exponential differential equations of semiabelian varieties
• Model theory.
• Strong splitting in stable homogeneous models
• A PSEUDOEXPONENTIAL-LIKE STRUCTURE ON THE ALGEBRAIC NUMBERS
• EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
• Exponential algebraicity in exponential fields
• A Combination of the Conjectures of Mordell-Lang and André-Oort
• A remark on Zilber's pseudoexponentiation
• On quasiminimal excellent classes
• Model theory of difference fields
• Covers of multiplicative groups of algebraically closed fields of arbitrary characteristic
• Quasiminimal structures and excellence
• Anomalous Subvarieties—Structure Theorems and Applications
• COVERS OF THE MULTIPLICATIVE GROUP OF AN ALGEBRAICALLY CLOSED FIELD OF CHARACTERISTIC ZERO

This page was built for publication: Exponentially closed fields and the conjecture on intersections with tori