Some remarks on the model theory of the complex exponential field.

Alex Wilkie (Manchester/Oxford)

Frank Adams 1,

Zilber has conjectured that the expansion of the field of complex numbers by the exponential function is quasi-minimal. I will comment briefly on a possible approach to this problem and on a special case for which this approach does work. I will then look more closely at the local obstructions to the general case. We will take advantage of the fact that complex quasi-varieties (ie the zero sets of systems of exponential-polynomial equations) have a very special local property, namely that their intersection with any ball of unit radius is UNIFORMLY definable in an o-minimal structure (to be specified in the talk). In particular, the extensive theory of p-valent complex analytic functions can be brought into play.

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