Submission date: 26 March 2010.

Abstract:

We show, assuming Schanuel's conjecture, that the complex field equipped with the complex exponentiation is existentially closed with respect to formulae of length 2 which yield an extension of predimension 0. That is, every irreducible complex polynomial in two variables where both variables appear, has infinitely many algebraically independent solutions of the form (z,e^z).

Mathematics Subject Classification: 03C45

Keywords and phrases: Model theory, Schanuel's conjecture

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