About Zilber's fields

Submitted by Vincenzo Mantova on Sun, 20/02/2011 - 16:56


British Postgraduate Model Theory Conference


University of Leeds




Friday, 21 January, 2011

Zilber's fields are imaginative algebraic structures which mimic the structure of the complex field equipped with the exponential function, but whose model-theoretic properties are well-known and rather well-behaved. Indeed, provided that we use a suitable infinitary language, their theory is axiomatizable, uncountably categorical and quasi-minimal. It is an open question if analogous properties hold for the classical complex exponential field, and if the complex field itself is just an example of Zilber's field. I will review some basic motivations for the use of Schanuel's Conjecture and existential closure in the definition of Zilber's fields, and I will show an easy way to explicitly build pseudoexponential functions which satisfy the axioms of Zilber's fields.