Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T06:57:32.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounds for covering numbers

Published online by Cambridge University Press:  12 March 2014

Andreas Liu
Andreas Liu*
Affiliation:
Department of Neurobiology, Harvard Medical School, 220 Longwood Avenue Boston, MA 02115, USA, E-mail: andreas_liu@hms.harvard.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Let λ be a singular cardinal of uncountable cofinality ν. Under various assumptions about the sizes of covering families for cardinals below λ, we prove upper bounds for the covering number COV(λ. λ. ν+. 2). This covering number is closely related to the cofinality of the partial order ([λ]ν. ⊆).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1303 - 1310
Copyright
Copyright © Association for Symbolic Logic 2006

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

[EHMR]Erdős, P., Hajnal, A., Maté, A., and Rado, R., Combinatorial set theory: Partition relations for cardinals, Studies in Logic and the Foundations of Mathematics, vol. 106, North Holland, Amsterdam, 1984.Google Scholar
[Gi]Gitik, M., Introduction to Prikry type forcing notions, to appear in Handbook of Set Theory.Google Scholar
[Liu]Liu, A., Reflecting pictures in cardinal arithmetic, Annals of Pure and Applied Logic, vol. 140 (2006), pp. 120–127.CrossRefGoogle Scholar
[Sh420]Shelah, S., Advances in cardinal arithmetic, Finite and infinite combinatorics in sets and logic, 1993, pp. 355–383.CrossRefGoogle Scholar
[Sh:g]Shelah, S., Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, Oxford, 1994.CrossRefGoogle Scholar
[Sh589]Shelah, S., Applications of pcf theory, this Journal, vol. 65 (2000), pp. 1624–1674.Google Scholar
[Sh460]Shelah, S., The generalized continuum hypothesis revisited, Israel Journal of Mathematics, vol. 116 (2000), pp. 285–321.CrossRefGoogle Scholar
[Sh829]Shelah, S., More on the revised GCH and the black box, Annals of Pure and Applied Logic, vol. 140 (2006), pp. 133–160.CrossRefGoogle Scholar