Ahuva C. Shkop's research while affiliated with Ben-Gurion University of the Negev and other places

Publications (5)

Article
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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 va...
Article
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.
Article
In this article, I will prove that assuming Schanuel's conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any such exponential polynomial. This implies a special case of Shapiro's conjecture: if p(x) and q...
Article
In 1984, Henson and Rubel [2] proved the following theorem: If p(x1,…, xn) is an exponential polynomial with coefficients in ℂ with no zeroes in ℂ, then p(x1,…, xn) = eg(x1,…, xn) where g(x1,…, xn) is some exponential polynomial over C. In this paper, I will prove the analog of this theorem for Zilber's Pseudoexponential fields directly from the ax...

Citations

... By the embeddability result, we also find that the resulting fields embed into all the Zilber fields of equal and larger cardinality. This is analogue to the result by Shkop [7], who proved that there are several real closed fields inside Zilber fields such that the restriction of the exponential to the real line is monotone. 12.1. ...
... Furthermore, F ∼ is unique up to isomorphism as an extension of F . Using the classification of strong extensions, we show that the Schanuel nullstellensatz, studied by D'Aquino, Terzo, and Macintyre [2] and also Shkop [13], is strictly weaker than the property of being strongly exponentially-algebraically closed (SEAC), and that SEAC fields are not model-complete. Zilber's pseudo-exponential fields are identified in Construction 7.1 as the strong exponential-algebraic closures of fields of rational functions in a set of indeterminates. ...