Partition numbers

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

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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DOI 10.1016/s0168-0072(97)00038-9
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References found in this work BETA

Happy Families.A. R. D. Mathias - 1977 - Annals of Pure and Applied Logic 12 (1):59.
Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.
Adjoining Dominating Functions.James E. Baumgartner & Peter Dordal - 1985 - Journal of Symbolic Logic 50 (1):94-101.
Partitions and Filters.P. Matet - 1986 - Journal of Symbolic Logic 51 (1):12-21.
Countable Filters on Ω.Otmar Spinas - 1999 - Journal of Symbolic Logic 64 (2):469-478.

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Citations of this work BETA

Antichains of Perfect and Splitting Trees.Paul Hein & Otmar Spinas - forthcoming - Archive for Mathematical Logic:1-22.
Around Splitting and Reaping for Partitions of Ω.Hiroaki Minami - 2010 - Archive for Mathematical Logic 49 (4):501-518.
Converse Dual Cardinals.Jörg Brendle & Shuguo Zhang - 2006 - Journal of Symbolic Logic 71 (1):22 - 34.
Countable Filters on Ω.Otmar Spinas - 1999 - Journal of Symbolic Logic 64 (2):469-478.

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