Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T08:34:05.042Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  12 March 2014

Heike Mildenberger  and
Saharon Shelah
Heike Mildenberger
Affiliation:
Abteilung für Mathematische Logik, Mathematisches Institut, Universität Freiburg, Eckerstr. 1, 79104 Freiburg im Breisgau, Germany, E-mail: heike.mildenberger@math.uni-freiburg.de
Saharon Shelah
Affiliation:
Einstein Institute of Mathematics, The Hebrew University, Edmond Safra Campus Givat Ram, Jerusalem 91904, Israel, E-mail: shelah@math.huji.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the statement in the title.

Keywords

forcing techniqueminimum cofinality of an ultrapowercofinality of the symmetric group
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1322 - 1340
Copyright
Copyright © Association for Symbolic Logic 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[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. 411–421.CrossRefGoogle Scholar
[2] Bartoszyński, Tomek and Judah, Haim, Set theory, on the structure of the real line, A K Peters, 1995.Google Scholar
[3] Baumgartner, James, Almost-disjoint sets, the dense-set problem, and the partition calculus, Annals of Mathematical Logic, vol. 9 (1976), pp. 401–439.CrossRefGoogle Scholar
[4] Blass, Andreas and Mildenberger, Heike, On the cofinality of ultrapowers, this Journal, vol. 64 (1999), pp. 727–736.Google Scholar
[5] Brendle, Jörg and Losada, Maria, The cofinality of the inifinite symmetric group and groupwise density, this Journal, vol. 68 (2003), no. 4, pp. 1354–1361.Google Scholar
[6] Canjar, Michael, Cofinalities of countable ultraproducts: The existence theorem, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 309–312.CrossRefGoogle Scholar
[7] Jech, Thomas, Set theory, The Third Millenium, revised and expanded ed., Springer, 2003.Google Scholar
[8] MacPherson, Dugald and Neumann, Peter, Subgroups of the infinite symmetric group, Journal of the London Mathematical Society, vol. 42 (1990), pp. 64–84.CrossRefGoogle Scholar
[9] Mildenberger, Heike and Shelah, Saharon, The relative consistency of g < cf(sym(ω)), this Journal, vol. 67 (2002), pp. 297–314.Google Scholar
[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. 2305–2317, [MdSh:894].CrossRefGoogle Scholar
[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. 60–71.CrossRefGoogle Scholar
[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. 33–45.CrossRefGoogle Scholar
[13] Shelah, Saharon, Groupwise density cannot be much bigger than the unbounded number, Mathematical Logic Quarterly, vol. 54 (2008), pp. 340–344.CrossRefGoogle Scholar
[14] Shelah, Saharon and Tsaban, Boaz, Critical cardinalities and additivity properties of combinatorial notions of smallness, Journal of Applied Analysis, vol. 9 (2003), pp. 149–162.CrossRefGoogle Scholar
[15] Thomas, Simon, Groupwise density and the cofinality of the infinite symmetric group, Archive for Mathematical Logic, vol. 37 (1998), pp. 483–493.CrossRefGoogle Scholar