A remark on strict independence relations

Archive for Mathematical Logic 55 (3-4):535-544 (2016)
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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 Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document}. We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document} has more than one strict independence relation. This answers a question of Adler :1–20, 2009, Question 1.7).

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Citations of this work

Neostability in countable homogeneous metric spaces.Gabriel Conant - 2017 - Annals of Pure and Applied Logic 168 (7):1442-1471.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
A geometric introduction to forking and thorn-forking.Hans Adler - 2009 - Journal of Mathematical Logic 9 (1):1-20.
Toward classifying unstable theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
Fundamentals of forking.Victor Harnik & Leo Harrington - 1984 - Annals of Pure and Applied Logic 26 (3):245-286.

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