FORCING CONSTRUCTIONS AND COUNTABLE BOREL EQUIVALENCE RELATIONS
SU GAO, Steve Jackson, Edward Krohne, Brandon Seward
Abstract
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.
Topics & Concepts
Borel equivalence relationCountable setMathematicsEquivalence relationEquivalence (formal languages)Borel hierarchyBorel setForcing (mathematics)Pure mathematicsBorel measureDiscrete mathematicsMathematical analysisProbability measureAdvanced Topology and Set TheoryComputability, Logic, AI AlgorithmsAdvanced Algebra and Logic