Implications

We have the following indirect implication of form equivalence classes:

423 \(\Rightarrow\) 373-n
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
423 \(\Rightarrow\) 373-n clear

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

Howard-Rubin Number Statement
423:

\(\forall n\in \omega-\{o,1\}\), \(C(\aleph_0, n)\) : For every \(n\in  \omega - \{0,1\}\), every denumerable set of \(n\) element sets has a choice function.

373-n:

(For \(n\in\omega\), \(n\ge 2\).) \(PC(\aleph_0,n,\infty)\): Every denumerable set of \(n\)-element sets has an infinite subset with a choice function.

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