PreprintarXiv licencearXiv
Borel-Tukey morphisms between Ramsey homogeneity relations
Abstract
We study Borel-Tukey morphisms between almost-homogeneity relations. For finite r,s≥1 and m,n≥2, we give the complete one-stage classification: Homrm→BTHomsn holds exactly when r>s, or when r=s and m≥ n. Our main result is that binary triple homogeneity requires exactly three sequential binary pair stages: Hom22;Hom22;Hom22⟶BTHom32 and Hom22;Hom22not⟶BTHom32. We also construct Borel morphisms Hom22;Hom23⟶BTHom32 and Hom22;Hom22⟶BTHom2k for every finite positive k.
Related
- Realizations of Countable Borel Equivalence Relations
- Finite-index extensions of essentially free countable Borel equivalence relations
- No Borel upper bound for the Fσ equivalence relations
- Ramsey properties of trees and C-relations via the partite construction
- On the continuity of the Tukey depth function for fuzzy data
BibTeX
@misc{goto2026boreltukey,
title = {{Borel-Tukey morphisms between Ramsey homogeneity relations}},
author = {Tatsuya Goto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23494},
eprint = {2609.23494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23494},
}
RIS
TY - UNPB
TI - Borel-Tukey morphisms between Ramsey homogeneity relations
AU - Tatsuya Goto
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.23494
UR - https://arxiv.org/abs/2609.23494
AB - We study Borel-Tukey morphisms between almost-homogeneity relations. For finite r,s≥1 and m,n≥2, we give the complete one-stage classification: Hom^r_m→_BTHom^s_n holds exactly when r>s, or when r=s and m≥ n. Our main result is that binary triple homogeneity requires exactly three sequential binary pair stages: Hom^2_2;Hom^2_2;Hom^2_2⟶_BTHom^3_2 and Hom^2_2;Hom^2_2not⟶_BTHom^3_2. We also construct Borel morphisms Hom^2_2;Hom^2_3⟶_BTHom^3_2 and Hom^2_2;Hom^2_2⟶_BTHom^2_k for every finite positive k.
ER -