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arXiv · 0708.1979

Advances in Cardinal Arithmetic

Saharon Shelah
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Abstract

If cf(kappa) = kappa, kappa^+< cf(lambda) = λ, then there is a stationary subset S of {delta , C_delta a club of lambda, otp(C_delta)=kappa, guessing clubs and for each alpha<lambda we have: {C_delta \cap alpha: alpha \in nacc(C_delta)} has cardinality <lambda. Also, we prove that e.g. there is a stationary subset of S_{<aleph_1}(lambda) of cardinality cf(S_{<aleph_1}(lambda),subseteq) Then we prove the existence of nice filters when instead being normal filters on omega_1 they are normal filters with larger domains, which can increase during a play. They can help us transfer situation on aleph_1-complete filters to normal ones

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Saharon Shelah. 2008-06-03. Advances in Cardinal Arithmetic. https://arxiv.org/abs/0708.1979

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