Martin's conjecture and strong ergodicity

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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.

Original languageEnglish (US)
Pages (from-to)749-759
Number of pages11
JournalArchive for Mathematical Logic
Issue number8
StatePublished - Nov 2009

All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic


  • Borel equivalence relation
  • Turing degree


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