Nonreduction of Relations in the Gromov Space to Polish Actions

Notre Dame Journal of Formal Logic 59 (2):205-213 (2018)
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Abstract

We show that in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov–Hausdorff distance cannot be reduced to the equivalence relation defined by any Polish action.

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References found in this work

A dichotomy theorem for turbulence.Greg Hjorth - 2002 - Journal of Symbolic Logic 67 (4):1520-1540.
A Dichotomy Theorem For Turbulence.Greg Hjorth - 2002 - Journal of Symbolic Logic 67 (4):1520-1540.

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