Implications

We have the following indirect implication of form equivalence classes:

378 \(\Rightarrow\) 11
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
378 \(\Rightarrow\) 11 clear

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.

11:

A Form of Restricted Choice for Families of Finite Sets: For every infinite set \(A\), \(A\) has an infinite subset \(B\) such that for every \(n\in\omega\), \(n>0\), the set of all \(n\) element subsets of \(B\) has a choice function. De la Cruz/Di Prisco [1998b]

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