Implications

We have the following indirect implication of form equivalence classes:

86-alpha \(\Rightarrow\) 351
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
86-alpha \(\Rightarrow\) 8 clear
8 \(\Rightarrow\) 351 Disasters in metric topology without choice, Keremedis, K. 2002, Comment. Math. Univ. Carolinae

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
86-alpha:

\(C(\aleph_{\alpha},\infty)\): If \(X\) is a set of non-empty sets such that \(|X| = \aleph_{\alpha }\), then \(X\) has a choice function.

8:

\(C(\aleph_{0},\infty)\):

351:

A countable product of metrizable spaces is metrizable.

Comment:

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