Exponential Fields Notes for Oxford Advanced Logic Class

Boris Zilber constructed his pseudo-exponential field Kexp, and proved that it is uncountably categorical in an appropriate logic. His methods were tailored to proving this particular theorem. My inten-tion is to develop some of the general theory of exponential fields far enough to prove an ℵ0-stability result which is the main idea behind the categoricity. I hope to explain how Kexp arises as a natural al-gebraic object. I may even get as far as proving ℵ1-categoricity. At least I should give the main ideas. A broader project is to construct a theory of Exponentially Alge-braically Closed Fields (EACF), an incomplete (but hopefully first-order) theory which would be analogous to ACVF, ACFA, etc. That is beyond the scope of these notes, but they should lay some of th