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Possible PCF algebras

Published online by Cambridge University Press:  12 March 2014

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
Corresponding

Abstract

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

(1) max Bα = α,

(2) if αBβ then BαBβ,

(3) if λα and λ is a limit ordinal then Bαλ 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, BαAn is finite.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Burke, M. and Magidor, M., Shelah's pcf theory and its applications, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 207254.CrossRefGoogle Scholar
[2]Jech, T., Singular cardinal problem: Shelah's theorem on , Bulletin of London Mathematical Society, vol. 24 (1992), pp. 127139.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. 213256.CrossRefGoogle Scholar
[5]Shelah, S., Cardinal arithmetic for skeptics, Bulletin of the American Mathematical Society, vol. 26 (1992), pp. 197210.CrossRefGoogle Scholar
[6]Shelah, S., Cardinal arithmetic, Oxford Logic Guides, no. 29, Oxford University Press, 1994.Google 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. 169194.CrossRefGoogle Scholar

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