Skip to main content Accessibility help
×
Home

The minimal cofinality of an ultrapower of ω and the cofinality of the symmetric group can be larger than b+

  • Heike Mildenberger (a1) and Saharon Shelah (a2)

Abstract

We prove the statement in the title.

Copyright

References

Hide All
[1] Banakh, Taras, Repovš, Dušan, and Zdomskyy, Lyubomyr, On the length of chain of proper subgroups covering a topological group, Archive for Mathematical Logic, vol. 50 (2011), no. 3–4, pp. 411421.
[2] Bartoszyński, Tomek and Judah, Haim, Set theory, on the structure of the real line, A K Peters, 1995.
[3] Baumgartner, James, Almost-disjoint sets, the dense-set problem, and the partition calculus, Annals of Mathematical Logic, vol. 9 (1976), pp. 401439.
[4] Blass, Andreas and Mildenberger, Heike, On the cofinality of ultrapowers, this Journal, vol. 64 (1999), pp. 727736.
[5] Brendle, Jörg and Losada, Maria, The cofinality of the inifinite symmetric group and groupwise density, this Journal, vol. 68 (2003), no. 4, pp. 13541361.
[6] Canjar, Michael, Cofinalities of countable ultraproducts: The existence theorem, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 309312.
[7] Jech, Thomas, Set theory, The Third Millenium, revised and expanded ed., Springer, 2003.
[8] MacPherson, Dugald and Neumann, Peter, Subgroups of the infinite symmetric group, Journal of the London Mathematical Society, vol. 42 (1990), pp. 6484.
[9] Mildenberger, Heike and Shelah, Saharon, The relative consistency of g < cf(sym(ω)), this Journal, vol. 67 (2002), pp. 297314.
[10] Mildenberger, Heike, The principle of near coherence of filters does not imply the filter dichotomy principle, Transactions of the American Mathematical Society, vol. 361 (2009), pp. 23052317, [MdSh:894].
[11] Mildenberger, Heike, Shelah, Saharon, and Tsaban, Boaz, Covering the Baire space with meager sets, Annals of Pure and Applied Logic, vol. 140 (2006), pp. 6071.
[12] Sharp, James D. and Thomas, Simon, Unbounded families and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 34 (1995), pp. 3345.
[13] Shelah, Saharon, Groupwise density cannot be much bigger than the unbounded number, Mathematical Logic Quarterly, vol. 54 (2008), pp. 340344.
[14] Shelah, Saharon and Tsaban, Boaz, Critical cardinalities and additivity properties of combinatorial notions of smallness, Journal of Applied Analysis, vol. 9 (2003), pp. 149162.
[15] Thomas, Simon, Groupwise density and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 37 (1998), pp. 483493.

Keywords

Related content

Powered by UNSILO

The minimal cofinality of an ultrapower of ω and the cofinality of the symmetric group can be larger than b+

  • Heike Mildenberger (a1) and Saharon Shelah (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.