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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).
Archive for Mathematical Logic – Springer Journals
Published: Mar 14, 2016
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