A note on the axioms for Zilber's pseudo-exponential fields

Details A note on the axioms for Zilber's pseudo-exponential fields A note on the axioms for Zilber's pseudo-exponential fields

2010-06-04

arxiv.org/abs/1006.0894v2

Mathematics

Logic

10 pages, v2: substantial alterations

Scientific paper

We show that Zilber's conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an example of a non-finitary abstract elementary class, answering a question of Kes\"al\"a and Baldwin.

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