Álvarez López, Jesús AntonioCandel, Alberto2024-02-012024-02-012018-01-08Álvarez López, J.A., Candel, A. (2018). Non-reduction of relations in the Gromov space to Polish actions. "Notre Dame J. Formal Logic", vol. 59, 205-2130029-4527http://hdl.handle.net/10347/32174We show that in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by the existence of coarse quasi-isometries or being at finite Gromov–Hausdorff distance cannot be reduced to the equivalence relation defined by any Polish action.eng© 2018 University of Notre DameGromov spaceGromov–Hausdorff metricquasi-isometry110206 Fundamentos de matemáticasjournal article10.1215/00294527-2017-0026open access