Independence relations for exponential fields

Aslanyan, Vahagn, Henderson, Robert, Kamsma, Mark and Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107 (2023) Independence relations for exponential fields. Annals of Pure and Applied Logic, 174 (8). ISSN 0168-0072

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Abstract

We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, showing that two of these are NSOP1-like and non-simple, a third is stable, and the fourth is the quasiminimal pregeometry of Zilber's exponential fields, previously known to be stable (and uncountably categorical). We also characterise the fourth independence relation in terms of the third, strong independence.

Item Type:	Article
Additional Information:	Funding Information: VA and JK were supported by EPSRC grant EP/S017313/1. RH and MK were supported by PhD studentships from UEA. MK was also supported by EPSRC grant EP/W522314/1.
Uncontrolled Keywords:	independence relation,exponential field,ax-schanuel,abstract elementary class,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
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
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	16 May 2023 08:32
Last Modified:	07 Nov 2024 12:46
URI:	https://ueaeprints.uea.ac.uk/id/eprint/92064
DOI:	10.1016/j.apal.2023.103288

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