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

Jonathan Kirby

doi:10.1215/00294527-2143844

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arXiv · 1006.0894

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

Jonathan Kirby

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Abstract

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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Jonathan Kirby. 2010-06-04. A note on the axioms for Zilber's pseudo-exponential fields. https://doi.org/10.1215/00294527-2143844

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