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Nonreduction of Relations in the Gromov Space to Polish Actions
Notre Dame Journal of Formal Logic 59 (2):205-213 (2018)
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.Links
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Citations of this work
Complexity of distances: Theory of generalized analytic equivalence relations.Marek Cúth, Michal Doucha & Ondřej Kurka - 2022 - Journal of Mathematical Logic 23 (1).
References found in this work
Cofinal families of Borel equivalence relations and quasiorders.Christian Rosendal - 2005 - Journal of Symbolic Logic 70 (4):1325-1340.
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