THE COFINALITY OF THE SYMMETRIC GROUP AND THE ...

THE COFINALITY OF THE SYMMETRIC GROUP AND THE COFINALITY OF ULTRAPOWERS HEIKE MILDENBERGER AND SAHARON SHELAH Abstract. We prove that mcf < cf(Sym(ω))) and mcf > cf(Sym(ω)) = b are both consistent relative to ZFC. This answers a question by Banakh, Repovˇs and Zdomskyy and a question from [12].

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revision:2014-04-28

modified:2014-04-28

1. Introduction The two cardinals mcf, the minimal cofinality cf((ω,