Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T22:52:14.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Mad families, splitting families and large continuum

Published online by Cambridge University Press:  12 March 2014

Jörg Brendle  and
Vera Fischer
Jörg Brendle
Affiliation:
Graduate School of System Informatics, Kobe University, Rokko-Dai 1-1, Nada-Ku, Kobe 657-8501, Japan, E-mail: [email protected]
Vera Fischer
Affiliation:
Kurt Gödel Research Center, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of . If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 198 - 208
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]Baumgartner, J. and Dordal, P., Adjoining dominating functions, this Journal, vol. 50 (1985), pp. 94–101.Google Scholar
[2]Blass, A., Combinatorial cardinal characteristics of the continuum, Handbook of set theory (Foreman, Matthew and Kanamori, Akihiro, editors), vol. 1, Springer, 2010, pp. 395–490.CrossRefGoogle Scholar
[3]Blass, A. and Shelah, S., Ultrafilters with small generating sets, Israel Journal of Mathematics, vol. 65 (1984), pp. 259–271.CrossRefGoogle Scholar
[4]Brendle, J., Mob families and mad families, Archive for Mathematical Logic, vol. 37 (1998), pp. 183–197.CrossRefGoogle Scholar
[5]Brendle, J., Mad families and ultrafilters, Acta Universitatis Carottnae. Mathematica et Physica, vol. 49 (2007), pp. 19–35.Google Scholar
[6]Fischer, V., The consistency of arbitrarily large spread between the bounding and the splitting numbers, doctoral dissertation, York University, 2008.Google Scholar
[7]Fischer, V. and Steprāns, J., The consistency of , Fundamenta Mathematicae, vol. 201 (2008), pp. 283–293.CrossRefGoogle Scholar
[8]Hechler, S., Short complete nested sequences in βℕ/ℕ and small maximal almost-disjoint families, General Topology and its Applications, vol. 2 (1972), pp. 139–149.CrossRefGoogle Scholar
[9]Shelah, S., On cardinal invariants of the continuum, Contemporary Mathematics, vol. 31 (1984), pp. 184–207.Google Scholar
[10]Shelah, S., Two cardinal invariants of the coninuum and FS linearly ordered iterated forcing, Acta Mathematica, vol. 192 (2004), pp. 187–223.CrossRefGoogle Scholar