Published online by Cambridge University Press: 12 March 2014
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.
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