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

Halbeisen, Lorenz

Math. Log. Q. 44, No. 1, 123-134 (1998).

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

Keywords:

partition properties; cardinal invariants; dualizations; dual-Mathias forcing

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