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

Kirby, J ORCID: https://orcid.org/0000-0003-4031-9107 (2013) A note on the axioms for Zilber's pseudo-exponential fields. Notre Dame Journal of Formal Logic, 54 (3-4). pp. 509-520.

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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.

Item Type:	Article
Uncontrolled Keywords:	pseudo-exponentiation,exponential fields,schanuel property,first-order theory,abstract elementary class
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Jonathan Kirby
Date Deposited:	27 Jan 2013 21:05
Last Modified:	07 Nov 2024 12:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/39549
DOI:	10.1215/00294527-2143844

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