Henson and Rubel's theorem for Zilber's Pseudoexponentiation

Ahuva C. Shkop

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In 1984, Henson and Rubel [2] proved the following theorem: If p(x 1.....x n) is an exponential polynomial with coefficients in ℂ with no zeroes in ℂ, then p(x 1.....x n) = e g(x 1.........x n) where g(x 1..... x n) 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 axioms. Furthermore, this proof relies only on the existential closedness axiom without any reference to Schanuel's conjecture.

Original languageEnglish
Pages (from-to)423-432
Number of pages10
JournalJournal of Symbolic Logic
Issue number2
StatePublished - 1 Jun 2012

ASJC Scopus subject areas

  • Philosophy
  • Logic


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