Partition forcing

18.03.2021 15:00 - 16:30

Jaroslav Šupina (Pavol Jozef Šafárik University in Košice, Slovakia)

A. Miller introduced in 1980 a forcing notion we refer to as a partition forcing.  Although it is a variant of Sacks' perfect set forcing, it is closely related to Miller's rational perfect set forcing.

The talk is devoted to our application of partition forcing in a proof of consistency of \(\mathfrak{u}=\mathfrak{i}<\mathfrak{a}_T\). Here, \(\mathfrak{i}\) is the minimal cardinality of a maximal independent family, \(\mathfrak{u}\) a minimal size of an ultrafilter base, and \(\mathfrak{a}_T\) is the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of \(2^{<\omega}\).

This is a joint work with Vera Fischer.



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