Independence relations for exponential fields

Vahagn Aslanyan; Robert Henderson; Mark Kamsma; Jonathan Kirby

doi:10.1016/j.apal.2023.103288

Independence relations for exponential fields

Vahagn Aslanyan, Robert Henderson, Mark Kamsma, Jonathan Kirby

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	103288
Journal	Annals of Pure and Applied Logic
Volume	174
Issue number	8
Early online date	15 May 2023
DOIs	https://doi.org/10.1016/j.apal.2023.103288
Publication status	E-pub ahead of print - 15 May 2023

Keywords

Independence relation
exponential field
Ax-Schanuel
abstract elementary class

Access to Document

10.1016/j.apal.2023.103288Licence: CC BY

indep-exp-revisionAccepted author manuscript, 454 KBLicence: CC BY

Cite this

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AU - Kirby, Jonathan

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N2 - 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.

AB - 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.

KW - Independence relation

KW - exponential field

KW - Ax-Schanuel

KW - abstract elementary class

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M3 - Article

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

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