Algebraic types in Zilber's exponential field

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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References in corpus (8)

• On Quasiminimal Excellent Classes
• Exponential algebraicity in exponential fields
• Exponentially Closed Fields and the Conjecture on Intersections with Tori
• Pseudo-exponential maps, variants, and quasiminimality
• Locally Polynomially Bounded Structures
• A note on the axioms for Zilber's pseudo-exponential fields
• Finitely Presented Exponential Fields
• The algebraic numbers definable in various exponential fields