Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T06:53:54.662Z Has data issue: false hasContentIssue false
  • English
  • Français

Two weak consequences of 0#

Published online by Cambridge University Press:  12 March 2014

M. Gitik ,
M. Magidor  and
H. Woodin
M. Gitik
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
M. Magidor
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel
H. Woodin
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proven that the following statement:

“there exists a club C ⊆ κ such that every α ∈ C is an inaccessible cardinal in L and, for every δ a limit point of C, C ∩ δ is almost contained in every club of δ of L”

is equiconsistent with a weakly compact cardinal if δ = ℵ1, and with a weakly compact cardinal of order 1 if δ = ℵ2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 3 , September 1985 , pp. 597 - 603
Copyright
Copyright © Association for Symbolic Logic 1985

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

[B]Baumgartner, J., A new class of order types, Annals of Mathematical Logic, vol. 9 (1976), pp. 187–222.CrossRefGoogle Scholar
[B-H-K]Baumgartner, J., Harrington, L. and Kleinberg, E., Adding a closed unbounded set, this Journal, vol. 41 (1976), pp. 481–482.Google Scholar
[D]Devlin, K., Aspects of constructibility, Lecture Notes in Mathematics, vol. 354, Springer-Verlag, Berlin, 1973.CrossRefGoogle Scholar
[D-J]Devlin, K. and Johnsbråten, H., The Souslin problem, Lecture Notes in Mathematics, vol. 405, Springer-Verlag, Berlin, 1974.CrossRefGoogle Scholar
[G-S]Gitik, M. and Shelah, S., On the □-condition, Israel Journal of Mathematics, vol. 48 (1984), pp. 148–158.CrossRefGoogle Scholar
[J]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[R]Radin, L., Adding closed cofinal sequences to large cardinals, Annals of Mathematical Logic, vol. 23 (1982), pp. 263–283.Google Scholar
[S]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar