Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
378 \(\Rightarrow\) 132 Weak choice principles, De la Cruz, O. 1998a, Proc. Amer. Math. Soc.

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

Howard-Rubin Number Statement
378:

Restricted Choice for Families of Well Ordered Sets:  For every infinite set \(X\) there is an infinite subset \(Y\) of \(X\) such that the family of non-empty well orderable subsets of \(Y\) has a choice function.

132:

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

Comment:

Back