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More on Cichoń's diagram and infinite games

Published online by Cambridge University Press:  12 March 2014

Masaru Kada
Masaru Kada*
Affiliation:
Department of Mathematics, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
*
Department of Computer Sciences, Kitami Institute of Technology, Kitami, Hokkaido 090-8507, Japan, E-mail:kada@math.cs.kitami-it.ac.jp
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Abstract

Some cardinal invariants from Cichoń's diagram can be characterized using the notion of cut-and-choose games on cardinals. In this paper we give another way to characterize those cardinals in terms of infinite games. We also show that some properties for forcing, such as the Sacks Property, the Laver Property and ωω-boundingness, are characterized by cut-and-choose games on complete Boolean algebras.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1713 - 1724
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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