In this paper, we explore some of the consequences of Martin's Conjecture on degree invariant Borel maps. These include the strongest conceivable ergodicity result for the Turing equivalence relation with respect to the filter on the degrees generated by the cones, as well as the statement that the complexity of a weakly universal countable Borel equivalence relation always concentrates on a null set.
All Science Journal Classification (ASJC) codes
- Borel equivalence relation
- Turing degree