The cofinality of the symmetric group and the cofinality of ultrapowers

by Mildenberger and Shelah. [MdSh:1021]

We prove that {{lowercase {mcf}}} < cf ({{Sym}(omega)}) and {{lowercase {mcf}}} > cf ({{Sym}(omega)})= {{lowercase {b}}} are both consistent relative to {sf ZFC}. This answers a question from [BanakhRepovsZdomskyy] and from [MdSh:967].


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