Algebraic types in Zilber's exponential field

Vahagn Aslanyan; Jonathan Kirby

doi:10.2140/mt.2025.4.37

Algebraic types in Zilber's exponential field

Vahagn Aslanyan, Jonathan Kirby

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

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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
Pages (from-to)	37-54
Number of pages	18
Journal	Model Theory
Volume	4
Issue number	1
DOIs	https://doi.org/10.2140/mt.2025.4.37
Publication status	Published - Jan 2025

Keywords

math.LO
math.NT
03C60 (primary)
algebraic closure
exponential field
Zilber’s pseudoexponential field
03C65
12L12

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10.2140/mt.2025.4.37

2405.01399v2Accepted author manuscript, 230 KB

http://arxiv.org/pdf/2405.01399v2

Cite this

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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. ",

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Algebraic types in Zilber's exponential field

Abstract

Keywords

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Exponentially Algebraically closed fields.

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Algebraic types in Zilber's exponential field

Abstract

Keywords

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Exponentially Algebraically closed fields.

Cite this