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The cofinality of the infinite symmetric group and groupwise density

Published online by Cambridge University Press:  12 March 2014

Jörg Brendle  and
Maria Losada
Jörg Brendle
Affiliation:
The Graduate School of Science and Technology, Kobe University, Rokko–Dai 1–1, Nada–Ku, Kobe 657-8501, Japan, E-mail: brendle@kurt.cla.kobe-u.ac.jp
Maria Losada
Affiliation:
The Graduate School of Science and Technology, Kobe University, Rokko-Dai 1–1, Nada–Ku, Kobe 657–8501, Japan Center of Research, Antonio Nariño University, Calle 20 Sur, NO. 13-61, Bogota, Colombia, E-mail: mel@uvmail.uanarino.edu.co
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Abstract

We show that g ≤ c(Sym(ω)) where g is the groupwise density number and c(Sym(ω)) is the cofinality of the infinite symmetric group. This solves (the second half of) a problem addressed by Thomas.

Keywords

infinite symmetric groupchains of subgroupscofinality of a groupcardinal invariants of the continuumgroupwise density
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1354 - 1361
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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