Implications

We have the following indirect implication of form equivalence classes:

391 \(\Rightarrow\) 165
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
391 \(\Rightarrow\) 392 clear
392 \(\Rightarrow\) 393 clear
393 \(\Rightarrow\) 165 clear

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

Howard-Rubin Number Statement
391:

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

392:

\(C(LO,LO)\): Every linearly ordered set of linearly orderable sets has a choice function.

393:

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

165:

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

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