Combinatorial aspects of the splitting number

by Garti and Shelah. [GaSh:962]
Annals Combinatorics, 2012
We prove that the existence of strong splitting families is equivalent to the failure of the polarized relation {{s} choose omega}-> {{s} choose {omega}^{1,1}_2} . We show that both directions are consistent with ZFC, and that the strong splitting number equals to the splitting number, when exists. Consequently, we can put some restriction on the possibility that {s} is singular.

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