Partition numbers

Annals of Pure and Applied Logic 90 (1-3):243-262 (1997)
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Abstract

We continue [21] and study partition numbers of partial orderings which are related to /fin. In particular, we investigate Pf, be the suborder of /fin)ω containing only filtered elements, the Mathias partial order M, and , ω the lattice of partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for Pf. We show that the partition number of is C. We also show that consistently the distributivity number of ω is smaller than the distributivity number of /fin. We also investigate partitions of a Polish space into closed sets. We show that such a partition either is countable or has size at least D, where D is the dominating number. We also show that the existence of a dominating family of size 1 does not imply that a Polish space can be partitioned into 1 many closed sets

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Citations of this work

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Antichains of perfect and splitting trees.Paul Hein & Otmar Spinas - 2020 - Archive for Mathematical Logic 59 (3-4):367-388.
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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Adjoining dominating functions.James E. Baumgartner & Peter Dordal - 1985 - Journal of Symbolic Logic 50 (1):94-101.
Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.
Partitions and filters.P. Matet - 1986 - Journal of Symbolic Logic 51 (1):12-21.
Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.

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