ALGEBRAIC TYPES IN ZILBER’S EXPONENTIAL FIELD

Vahagn Aslanyan; Jonathan Kirby

doi:10.2140/mt.2025.4-1

ALGEBRAIC TYPES IN ZILBER’S EXPONENTIAL FIELD

Vahagn Aslanyan, Jonathan Kirby

Pure Mathematics

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

Abstract

We characterise the model-theoretic algebraic closure in Zilber’s exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof.

Original language	English
Journal	Model Theory
DOIs	https://doi.org/10.2140/mt.2025.4-1
Publication status	Published - 1 Jan 2025

Keywords

Exponential field
Zilber’s pseudoexponential field
algebraic closure

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10.2140/mt.2025.4-1

acl_B_expAccepted author manuscript, 363 KBLicence: CC BY

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title = "ALGEBRAIC TYPES IN ZILBER{\textquoteright}S EXPONENTIAL FIELD",

abstract = "We characterise the model-theoretic algebraic closure in Zilber{\textquoteright}s exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof.",

keywords = "Exponential field, Zilber{\textquoteright}s pseudoexponential field, algebraic closure",

author = "Vahagn Aslanyan and Jonathan Kirby",

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AU - Kirby, Jonathan

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N2 - We characterise the model-theoretic algebraic closure in Zilber’s exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof.

AB - We characterise the model-theoretic algebraic closure in Zilber’s exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof.

KW - Exponential field

KW - Zilber’s pseudoexponential field

KW - algebraic closure

U2 - 10.2140/mt.2025.4-1

DO - 10.2140/mt.2025.4-1

M3 - Article

SN - 2832-9058

JO - Model Theory

JF - Model Theory

ER -

ALGEBRAIC TYPES IN ZILBER’S EXPONENTIAL FIELD

Abstract

Keywords

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