### 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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