Submission date: 14 December 2015

Abstract:

We give a construction of quasiminimal fields equipped with pseudo-analytic functions, generalising Zilber's pseudo-exponential function and correcting some errors. In particular we construct pseudo-Weierstrass p-functions and generic power functions. For each structure we give uncountably categorical axioms. We show that the complex field with the corresponding analytic function is isomorphic to the pseudo-analytic version if and only the appropriate version of Schanuel's conjecture is true and a corresponding strong $\Gamma$-closedness property holds. As an application we show that the complex exponential field is quasiminimal under the much weaker hypothesis that it is generically strongly exponentially-algebraically closed, without the assumption of Schanuel's conjecture.

Mathematics Subject Classification: 03C65, 03C60, 03C75

Keywords and phrases:

Full text arXiv 1512.04262: pdf, ps.