Marked Groups with Isomorphic Cayley Graphs but Different Borel Combinatorics

Published 6 Oct 2018 in math.LO | (1810.03062v2)

Abstract: We construct pairs of marked groups with isomorphic Cayley graphs but different Borel chromatic numbers for the free parts of their shift graphs. This answers a question of Kechris and Marks. We also show that these graphs have different Baire measurable and measure chromatic numbers, answering analogous versions of the question.

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Felix Weilacher

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