Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
60 \(\Rightarrow\) 45-n clear
45-n \(\Rightarrow\) 33-n clear
33-n \(\Rightarrow\) 47-n clear

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

Howard-Rubin Number Statement
60:

\(C(\infty,WO)\): Every set of non-empty, well orderable sets has a choice function.
Moore, G. [1982], p 125.

45-n:

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

33-n:

If \(n\in\omega-\{0,1\}\), \(C(LO,n)\):  Every linearly ordered set of \(n\) element 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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