arXiv subjects

Ahuva C. Shkop

Publications and source records attributed to Ahuva C. Shkop.

4 recordsLinked to original sources

arXiv2013

A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields

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.

math.LO↗

arXiv2011

Real Closed Exponential Subfields of Pseudoexponential Fields

In this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field satisfying Schanuel's conjecture.

math.LO↗

arXiv2009

Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials

In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions. This implies a positive answer to Shapiro's conjecture for exponential polynomials over the algebraic numbers for pseudoexponential fields as well as for any algebraically closed exponential field satisfying Schanuel's conjecture.

math.LO↗

arXiv2009

Henson and Rubel's Theorem for Zilber's Pseudoexponentiation

This paper contains an alternate proof of the Schanuel Nullstellensatz for Zilber's Pseudoexponentiation. Furthermore, in an algebraically closed exponential field whose exponential map is surjective with standard kernel, this property follows from the field being exponentially algebraically closed.

math.LO↗