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

Logic

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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.

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	Published - Aug 2023

Keywords

Independence relation
exponential field
Ax-Schanuel
abstract elementary class

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10.1016/j.apal.2023.103288Licence: CC BY

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

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title = "Independence relations for exponential fields",

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.",

keywords = "Independence relation, exponential field, Ax-Schanuel, abstract elementary class",

author = "Vahagn Aslanyan and Robert Henderson and Mark Kamsma and Jonathan Kirby",

note = "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.",

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doi = "10.1016/j.apal.2023.103288",

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T1 - Independence relations for exponential fields

AU - Aslanyan, Vahagn

AU - Henderson, Robert

AU - Kamsma, Mark

AU - Kirby, Jonathan

N1 - 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.

PY - 2023/8

Y1 - 2023/8

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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U2 - 10.1016/j.apal.2023.103288

DO - 10.1016/j.apal.2023.103288

M3 - Article

VL - 174

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 8

M1 - 103288

ER -

Independence relations for exponential fields

Abstract

Keywords

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Exponentially Algebraically closed fields.

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Independence relations for exponential fields

Abstract

Keywords

Access to Document

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Projects

Exponentially Algebraically closed fields.

Cite this