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The cofinality of the infinite symmetric group and groupwise density
Journal of Symbolic Logic 68 (4):1354-1361 (2003)
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 ThomasLinks
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Citations of this work
Cardinal invariants related to permutation groups.Bart Kastermans & Yi Zhang - 2006 - Annals of Pure and Applied Logic 143 (1-3):139-146.
Groupwise density cannot be much bigger than the unbounded number.Saharon Shelah - 2008 - Mathematical Logic Quarterly 54 (4):340-344.
References found in this work
Asymptotic probabilities of extension properties and random l -colourable structures.Vera Koponen - 2012 - Annals of Pure and Applied Logic 163 (4):391-438.
Groupwise density and the cofinality of the infinite symmetric group.Simon Thomas - 1998 - Archive for Mathematical Logic 37 (7):483-493.
Uniformization Problems and the Cofinality of the Infinite Symmetric Group.James D. Sharp & Simon Thomas - 1994 - Notre Dame Journal of Formal Logic 35 (3):328-345.
Unbounded families and the cofinality of the infinite symmetric group.James D. Sharp & Simon Thomas - 1995 - Archive for Mathematical Logic 34 (1):33-45.
Isolating cardinal invariants.Jindřich Zapletal - 2003 - Journal of Mathematical Logic 3 (1):143-162.
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