Advances in Cardinal Arithmetic
Abstract
If cf(kappa) = kappa, kappa+< cf(lambda) = λ, then there is a stationary subset S of delta<lambda:cf(delta)=kappa in I[lambda]. Moreover, we can find <Cdelta :delta in S>, Cdelta a club of lambda, otp(Cdelta)=kappa, guessing clubs and for each alpha<lambda we have: Cdelta alpha: alpha ∈ nacc(Cdelta) has cardinality <lambda. Also, we prove that e.g. there is a stationary subset of S<aleph1(lambda) of cardinality cf(S<aleph1(lambda),subseteq) Then we prove the existence of nice filters when instead being normal filters on omega1 they are normal filters with larger domains, which can increase during a play. They can help us transfer situation on aleph1-complete filters to normal ones
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