Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number ��. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to the splitting number �� coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics.
This is the accepted version of the following article:
Coskey, S. & Schneider, S. (2017). Cardinal Characteristics and Countable Borel Equivalence Relations. Mathematical Logic Quarterly, 63(3-4), 211-227.
which has been published in final form at doi: 10.1002/malq.201400111
Coskey, Samuel and Schneider, Scott. (2017). "Cardinal Characteristics and Countable Borel Equivalence Relations". Mathematical Logic Quarterly, 63(3-4), 211-227. https://doi.org/10.1002/malq.201400111