Forcing constructions and countable Borel equivalence relations
Su Gao, Steve Jackson, Edward Krohne, Brandon Seward
TL;DR
This paper explores the use of forcing techniques to analyze countable Borel equivalence relations, uncovering hidden regularities and establishing nonexistence results for certain Borel complete sections.
Contribution
It introduces forcing-based methods to study Borel equivalence relations, revealing new regularity properties and nonexistence results for specific Borel sections.
Findings
Revealed hidden regularity properties of Borel complete sections
Proved nonexistence of Borel complete sections with certain features
Applied forcing techniques to analyze orbit structures
Abstract
We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain features.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis