Title: A Note on Schanuel's Conjectures for Exponential Fields
Abstract: In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of complex numbers [11, page 30]. In this article, we derive from Ax's theorem transcendency results in the context of differential valued exponential fields. In particular, we obtain results for exponential Hardy fields, Logarithmic-Exponential power series fields and Exponential-Logarithmic power series fields.
Publication Year: 2012
Publication Date: 2012-04-02
Language: en
Type: article
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