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Pair-splitting, pair-reaping and cardinal invariants of Fσ-ideals

Published online by Cambridge University Press:  12 March 2014

Michael Hrušák ,
David Meza-Alcántara  and
Hiroaki Minami
Michael Hrušák
Affiliation:
Instituto de Matemáticas, Unam, Apartado Postal 61-3, Xangari 58089, Morelia, michoacán, México. E-mail: michael@matmor.unam.mx
David Meza-Alcántara
Affiliation:
Instituto de Matemáticas, Unam, Apartado Postal 61-3, Xangari 58089, Morelia, michoacán, México. E-mail: dmeza@matmor.unam.mx
Hiroaki Minami
Affiliation:
Kurt Gödel Research Center for Mathematical Logic Währinger Straße 25 A-1090 Wien, Austria. E-mail: minami@kurt.scitec.kobe-u.ac.jp
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Abstract

We investigate the pair-splitting number which is a variation of splitting number, pair-reaping number which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of Fσ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.

Keywords

Pair-splitting numberpair-reaping numbercardinal invariants of the continuumFσ-idealsLaver forcing
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 661 - 677
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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