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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
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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

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References

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