Hostname: page-component-5b777bbd6c-cp4x8 Total loading time: 0 Render date: 2025-06-18T00:43:14.962Z Has data issue: false hasContentIssue false
  • English
  • Français

Possible PCF algebras

Published online by Cambridge University Press:  12 March 2014

Thomas Jech  and
Saharon Shelah
Thomas Jech
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail: jech@math.psu.edu
Saharon Shelah
Affiliation:
School of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail: shelah@math.huji.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

There exists a family of sets of countable ordinals such that:

(1) max Bα = α,

(2) if α ∈ Bβ then Bα ⊆ Bβ,

(3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ, β < α, and by the bounded subsets of λ,

(4) there is a partition of ω1 such that for every α and every n, Bα ∩ An is finite.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 313 - 317
Copyright
Copyright © Association for Symbolic Logic 1996

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Burke, M. 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., Singular cardinal problem: Shelah's theorem on , Bulletin of London Mathematical Society, vol. 24 (1992), pp. 127–139.CrossRefGoogle Scholar
[3]Shelah, S., Proper forcing, Lecture Notes in Mathematics, no. 940, Springer-Verlag, 1982.CrossRefGoogle Scholar
[4]Shelah, S., Successors of singulars, cofinalities of reduced products of cardinals and productivity of chain conditions, Isreal Journal of Mathematics, vol. 62 (1988), pp. 213–256.CrossRefGoogle Scholar
[5]Shelah, S., Cardinal arithmetic for skeptics, Bulletin of the American Mathematical Society, vol. 26 (1992), pp. 197–210.CrossRefGoogle Scholar
[6]Shelah, S., Cardinal arithmetic, Oxford Logic Guides, no. 29, Oxford University Press, 1994.CrossRefGoogle Scholar
[7]Shelah, S., Laflamme, C., and Hart, B., Models with second order properties V: A general principle, Annals of Pure and Applied Logic, vol. 64 (1993), pp. 169–194.CrossRefGoogle Scholar