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On shattering, splitting and reaping partitions. (English) Zbl 0896.03036

The author deals with cardinal invariants for the family of all partitions of \(\omega\). Especially he investigates dualizations of some well-known cardinal invariants for the power set of \(\omega\). So he considers the dual-shattering, dual-splitting and dual-reaping numbers. He shows that it is consistent with ZFC that the dual-shattering cardinal is greater than \(\omega_1\). This is done using dual-Mathias forcing.
Reviewer: M.Weese (Potsdam)

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
03C25 Model-theoretic forcing
05A18 Partitions of sets
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