## 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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### References:

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