A Schanuel property for exponentially transcendental powers

Abstract

We prove the analogue of Schanuel's conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case.

5 pages

References in corpus (2)

• Exponential algebraicity in exponential fields
• Locally Polynomially Bounded Structures

Cited by in corpus (9)

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• Exponential Sums Equations and Tropical Geometry
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• Combinatorial Bounds in Distal Structures
• Natural models of theories of green points
• Quasiminimality of complex powers
• Variants of Schanuel's conjecture
• Hilbert polynomials for finitary matroids