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Normality of a filter over a space of partitions

Published online by Cambridge University Press:  12 March 2014

Mark Fuller
Mark Fuller*
Affiliation:
Department of Mathematics, University of Wisconsin Center-Rock County, Janesville. Wisconsin 53546, E-mail: mfuller@uwcmail.uwc.edu
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Extract

In this paper we investigate the closure of certain filters under different definitions of diagonal intersection. The space of partitions over which filters concern us is Qκ(λ), the set of partitions of λ into fewer than κ pieces, invented by Henle and Zwicker [4] in the spirit of Pκ(λ). Various notions of normality for filters over Qκ(λ) have been introduced in [4] and [7]. Our objective is to find a notion of normality in terms of a tractable diagonal intersection which also in some sense reflects the construction of a partition. Extending the parallels between Pκ(λ) and Qκ(λ) we define two diagonal intersections, Δ1 and Δ2, under which the club filter is closed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 529 - 533
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

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