Possible PCF algebras

Journal of Symbolic Logic 61 (1):313-317 (1996)
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Abstract

There exists a family $\{B_\alpha\}_{\alpha of sets of countable ordinals such that: (1) max B α = α, (2) if α ∈ B β then $B_\alpha \subseteq B_\beta$ , (3) if λ ≤ α and λ is a limit ordinal then B α ∩ λ is not in the ideal generated by the $B_\beta, \beta , and by the bounded subsets of λ, (4) there is a partition {A n } ∞ n = 0 of ω 1 such that for every α and every n, B α ∩ A n is finite

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Shelah's pcf theory and its applications.Maxim R. Burke & Menachem Magidor - 1990 - Annals of Pure and Applied Logic 50 (3):207-254.

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