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A remark on strict independence relations

A remark on strict independence relations We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for $${T^{\rm eq}}$$ T eq . We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then $${T^{\rm eq}}$$ T eq has more than one strict independence relation. This answers a question of Adler (J Math Log 9(1):1–20, 2009, Question 1.7). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

A remark on strict independence relations

Archive for Mathematical Logic , Volume 55 (4) – Mar 14, 2016

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-016-0479-6
Publisher site
See Article on Publisher Site

Abstract

We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for $${T^{\rm eq}}$$ T eq . We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then $${T^{\rm eq}}$$ T eq has more than one strict independence relation. This answers a question of Adler (J Math Log 9(1):1–20, 2009, Question 1.7).

Journal

Archive for Mathematical LogicSpringer Journals

Published: Mar 14, 2016

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