Implications

We have the following indirect implication of form equivalence classes:

394 \(\Rightarrow\) 47-n
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
394 \(\Rightarrow\) 165 clear
165 \(\Rightarrow\) 122 clear
122 \(\Rightarrow\) 47-n clear

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

Howard-Rubin Number Statement
394:

\(C(WO,LO)\): Every well ordered set of non-empty linearly orderable sets has a choice function.

165:

\(C(WO,WO)\):  Every well ordered family of non-empty, well orderable sets has a choice function.

122:

\(C(WO,<\aleph_{0})\): Every well ordered set of non-empty finite sets has a choice function.

47-n:

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

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