Hostname: page-component-6bf8c574d5-nvqbz Total loading time: 0 Render date: 2025-03-07T22:49:36.046Z Has data issue: false hasContentIssue false
  • English
  • Français

Ultrafilters of character ω1

Published online by Cambridge University Press:  12 March 2014

Klaas Pieter Hart
Klaas Pieter Hart*
Affiliation:
Department of Mathematical Analysis, Šafárik University, Košice, Czechoslovakia Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
*
Department of Mathematics and Computer Science, Technische Hogeschool te Delft, 2600 AJ Delft, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

Using side-by-side Sacks forcing, it is shown that it is consistent that 2ω be large and that there be many types of ultrafilters of character ω1.

Keywords

Side-by-side Sacks forcingultrafilters of character ω1Rudin-Frolík order
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 1 - 15
Copyright
Copyright © Association for Symbolic Logic 1989

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

[Ba]Baumgartner, J. E., Sacks forcing and the total failure of Martin's axiom, Topology and Its Applications, vol. 19 (1985), pp. 211–225.CrossRefGoogle Scholar
[BaLa]Baumgartner, J. E. and Laver, R., Iterated perfect-set forcing, Annals of Mathematical Logic, vol. 17(1979), pp. 271–288.CrossRefGoogle Scholar
[BlSh]Blass, A. and Shelah, S., Near coherence of filters. III: A simplified consistency proof (to appear).Google Scholar
[BuBu]Bukovský, L. and Butkovičová, E., Ultrafilter with ℵ0 predecessors in Rudin-Frolik order, Commentationes Mathematicae Universitatis Carolinae, vol. 22 (1981), pp. 429–447.Google Scholar
[Bu1]Butkovičová, E., Gaps in Rudin-Frolík order, General topology and its relations to modern analysis and algebra, V (proceedings of the fifth Prague symposium), Heldermann, Berlin, 1983, pp. 56–58.Google Scholar
[Bu2]Butkovičová, E., Short branches in Rudin-Frolik order, Commentationes Mathematicae Universitatis Carolinae, vol. 26 (1985), pp. 631–635.Google Scholar
[CoVo]Copláková, E. and Vojtáš, P., A new sufficient condition for the existence of Q-points in βω − ω, Topology, theory and applications (Császár, Á., editor), Colloquia Mathematica Societatis János Bolyai, vol. 41, North-Holland, Amsterdam, 1985, pp. 199–208.Google Scholar
[vD]van Douwen, E. K., The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111–167.CrossRefGoogle Scholar
[Ku1]Kunen, K., Weak P-points in N*, Topology, II (Császár, Á., editor), Colloquia Mathematica Societatis János Bolyai, vol. 23, North-Holland, Amsterdam, 1980, pp. 741–749.Google Scholar
[Ku2]Kunen, K., Set theory, North-Holland, Amsterdam, 1980.Google Scholar
[Ku3]Kunen, K., letter to the author.Google Scholar
[La]Laver, R., Products of infinitely many perfect trees, Journal of the London Mathematical Society, ser. 2, vol. 29 (1984), pp. 385–396.CrossRefGoogle Scholar
[vM]van Mill, J., An introduction to βω, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 503–567.CrossRefGoogle Scholar
[Ru]Rudin, M. E., Partial orders on the types of βN, Transactions of the American Mathematical Society, vol. 155 (1971), pp. 353–362.Google Scholar
[Sh]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[S0]Solomon, R. C., A type in βN with ℵ0 relative types, Fundamenta Mathematicae, vol. 79 (1972), pp. 209–212.CrossRefGoogle Scholar