We prove that \(\mathfrak{mcf}\) and \(\mathfrak{mcf}\) are both consistent relative to ZFC. This answers a question by Banakh, Repovš and Zdomskyy and a question from [MS11].

中文翻译：

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对称群的共最终性与超大国的共最终性

我们证明\（\ mathfrak {mcf} \）和\（\ mathfrak {mcf} \）相对于ZFC都是一致的。这回答了Banakh，Repovš和Zdomskyy的问题以及[MS11]的问题。