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Possible PCF algebras

Published online by Cambridge University Press:  12 March 2014

Thomas Jech
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA, E-mail:
Saharon Shelah
School of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail:


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.

Research Article
Copyright © Association for Symbolic Logic 1996

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