Relative primeness and Borel partition properties for equivalence relations

@article{Clemens2020RelativePA,
  title={Relative primeness and Borel partition properties for equivalence relations},
  author={John D. Clemens},
  journal={Transactions of the American Mathematical Society},
  year={2020}
}
  • J. Clemens
  • Published 30 May 2020
  • Mathematics
  • Transactions of the American Mathematical Society
We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness. We introduce several analogues of cardinal properties for Borel equivalence relations, including the notion of a prime equivalence relation and Borel partition properties on quotient spaces. In particular, we introduce a notion of Borel weak compactness, and… 
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