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.
Preview |
PDF (nape2_4)
- Accepted Version
Download (315kB) | Preview |
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 |
UEA Research Groups: | Faculty of Science > Research Groups > Logic |
Depositing User: | Jonathan Kirby |
Date Deposited: | 27 Jan 2013 21:05 |
Last Modified: | 26 Mar 2023 06:30 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/39549 |
DOI: | 10.1215/00294527-2143844 |
Downloads
Downloads per month over past year
Actions (login required)
![]() |
View Item |