Axiom Of Choice

We have the following indirect implication of form equivalence classes:

349 \(\Rightarrow\) 350 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
349 \(\Rightarrow\) 350	clear

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

Howard-Rubin Number	Statement
349:	\(MC(\infty,\aleph_0)\): For every set \(X\) of non-empty denumerable sets there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\).
350:	\(MC(\aleph_0,\aleph_0)\): For every denumerable set \(X\) of non-empty denumerable sets there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\).

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