Possible PCF algebras
Thomas Jech, Saharon Shelah · Journal of Symbolic Logic · 1996
Abstract There exists a family of sets of countable ordinals such that: (1) maxBα=α, (2) ifα∈BβthenBα⊆Bβ, (3) ifλ≤αandλis a limit ordinal thenBα∩λis not in the ideal generated by theBβ,β<α, and by the bounded subsets ofλ, (4) there is a partition ofω1such that for everyαand everyn,Bα∩Anis finite.