Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
422-n \(\Rightarrow\) 47-n clear
47-n \(\Rightarrow\) 423 clear

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

Howard-Rubin Number Statement
422-n:

\(UT(WO,n,WO)\), \(n\in \omega-\{0,1\}\): The union of a well ordered set of \(n\) element sets can be well ordered.

47-n:

If \(n\in\omega-\{0,1\}\), \(C(WO,n)\): Every well ordered collection of \(n\)-element sets has a choice function.

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.

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