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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: [email protected]
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: [email protected]
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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

REFERENCES

[1] Blass, A and Laflamme, C, Consistency results about filters and the number of inequivalent growth types, this Journal, vol. 54 (1989), pp. 50–56.Google Scholar
[2] Macpherson, H. D. and Neumann, Peter M., Subgroups of infinite symmetric groups. Journal of the London Mathematical Society. Second Series, vol. 42 (1990), pp. 64–84.CrossRefGoogle Scholar
[3] Mildenberger, H. and Shelah, S., The relative consistency of g < c (Sym(w)), this Journal, vol. 67 (2002), pp. 297–314.Google Scholar
[4] Sharp, J. D. and Thomas, S., Uniformization problems and the cofinality of the infinite symmetric group, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 328–345.Google Scholar
[5] Sharp, J. D., Unbounded families and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 34 (1995), pp. 33–45.CrossRefGoogle Scholar
[6] Thomas, S., Groupwise density and the confinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 37 (1998), pp. 483–493.Google Scholar
[7] Zapletal, J., Isolating cardinal invariants, Journal of Mathematical Logic, vol. 3 (2003), pp. 143–162.Google Scholar