Notre Dame Journal of Formal Logic

Nonreduction of Relations in the Gromov Space to Polish Actions

Jesús A. Álvarez López and Alberto Candel

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 2 (2018), 205-213.

Dates
Received: 18 February 2015
Accepted: 5 October 2015
First available in Project Euclid: 8 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1515402015

Digital Object Identifier
doi:10.1215/00294527-2017-0026

Mathematical Reviews number (MathSciNet)
MR3778308

Zentralblatt MATH identifier
06870289

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
Secondary: 54H20: Topological dynamics [See also 28Dxx, 37Bxx] 54E50: Complete metric spaces

Keywords
Gromov space Gromov–Hausdorff metric quasi-isometry

Citation

Álvarez López, Jesús A.; Candel, Alberto. Nonreduction of Relations in the Gromov Space to Polish Actions. Notre Dame J. Formal Logic 59 (2018), no. 2, 205--213. doi:10.1215/00294527-2017-0026. https://projecteuclid.org/euclid.ndjfl/1515402015


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References

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