Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T01:36:36.673Z Has data issue: false hasContentIssue false
  • English
  • Français

Splitting number at uncountable cardinals

Published online by Cambridge University Press:  12 March 2014

Jindřich Zapletal
Jindřich Zapletal*
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail: zapletal@math.psu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We study a generalization of the splitting number s to uncountable cardinals. We prove that 𝔰(κ) > κ+ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption 𝔰(ℵω) > ℵω+1 has a considerable large cardinal strength as well.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 35 - 42
Copyright
Copyright © Association for Symbolic Logic 1997

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] Burke, M. R. and Magidor, M., Shelah's pcf theory and its applications, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 207–254.CrossRefGoogle Scholar
[2] Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[3] Kamo, S., Splitting numbers on uncountable regular cardinals, preprint.Google Scholar
[4] Kanamori, A., The higher infinite, Springer-Verlag, New York, 1994.Google Scholar
[5] Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcings, Israel Journal of Mathematics, vol. 29 (1978), pp. 385–388.CrossRefGoogle Scholar
[6] Mitchell, W., The core model for sequences of measures I, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95 (1984), pp. 41–58.CrossRefGoogle Scholar
[7] Mitchell, W., On the singular cardinal hypothesis, Transactions of the American Mathematical Society, vol. 329 (1992), pp. 507–530.CrossRefGoogle Scholar
[8] Suzuki, T., About splitting numbers, preprint.Google Scholar