Hyperfiniteness on Topological Ramsey Spaces

2024/12/02 by Bursics, Balázs, Vidnyánszky, Zoltán
#03E15 (Primary) 68Q17 (Secondary) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2412.01315

Abstract

We investigate the behavior of countable Borel equivalence relations (CBERs) on topological Ramsey spaces. First, we give a simple proof of the fact that every CBER on [ℕ]^ℕ is hyperfinite on some set of the form [A]^ℕ. Using the idea behind the proof, we show the analogous result for every topological Ramsey space.

Related

• The Borel Ramsey properties for countable Borel equivalence relations
• Topological Ramsey spaces of equivalence relations and a dual Ramsey\n theorem for countable ordinals
• Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of p-points
• An abstract approach in canonizing topological Ramsey spaces
• Every CBER is smooth below the Carlson-Simpson generic partition