There are a number of interesting open problems about definability in the field of complex numbers with exponentiation. Zilber has proposed a novel approach. He constructed a nonelementary class of exponential algebraically closed fields and showed that in this class definable subsets of the field are countable or co-countable. He also showed the class is categorical in all uncountable cardinalities. The natural question is whether the complex numbers are the unique model in this class of size continuum.
In this talk I will show that, assuming Schanuel's Conjecture, the simplest case of Zilber's strong exponential closure axiom is true in the complex numbers.