Algebraic types in Zilber's exponential field

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Aslanyan, Vahagn and Kirby, Jonathan (2025) Algebraic types in Zilber's exponential field. Model Theory, 4 (1). pp. 37-54. ISSN 2832-904X

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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.

Item Type: Article
Additional Information: Funding information: Most of this work was done while Aslanyan was a senior research associate at the University of East Anglia, where both authors were supported by EPSRC grant EP/S017313/1. Aslanyan has continued to work on this paper at the University of Leeds (supported by Leverhulme Trust Early Career Fellowship ECF-2022-082) and at the University of Manchester (supported by EPSRC Open Fellowship EP/X009823/1). Rights Retention Statement: For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission
Uncontrolled Keywords: math.lo,math.nt,03c60 (primary),algebraic closure,exponential field,zilber’s pseudoexponential field,03c65,12l12,logic,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School: Faculty of Science > School of Mathematics (former - to 2024)
Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups: Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Faculty of Science > Research Groups > Logic (former - to 2024)
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Depositing User: LivePure Connector
Date Deposited: 27 Nov 2024 10:47
Last Modified: 04 Nov 2025 12:31
URI: https://ueaeprints.uea.ac.uk/id/eprint/97783
DOI: 10.2140/mt.2025.4.37

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