The cofinality of the infinite symmetric group and groupwise density

Jörg Brendle; Maria Losada

doi:10.2178/jsl/1067620191

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.

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Jörg Brendle. Maria Losada. "The cofinality of the infinite symmetric group and groupwise density." J. Symbolic Logic 68 (4) 1354 - 1361, December 2003. https://doi.org/10.2178/jsl/1067620191

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Published: December 2003

First available in Project Euclid: 31 October 2003

zbMATH: 1070.03032

MathSciNet: MR2017359

Digital Object Identifier: 10.2178/jsl/1067620191

Subjects:

Primary: 03E17

Secondary: 20B30

Keywords: cardinal invariants of the continuum , chains of subgroups , cofinality of a group , groupwise density , infinite symmetric group

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