Implications

We have the following indirect implication of form equivalence classes:

380 \(\Rightarrow\) 132
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
380 \(\Rightarrow\) 132 clear

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

Howard-Rubin Number Statement
380:

\(PC(\infty,WO,\infty)\):  For every infinite family of non-empty well orderable sets, there is an infinite subfamily \(Y\) of \(X\) which has a choice function.

132:

\(PC(\infty, <\aleph_0,\infty)\):  Every infinite family of finite  sets has an infinite subfamily with a choice function.

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