Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
329 \(\Rightarrow\) 349 clear

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

Howard-Rubin Number Statement
329:

\(MC(\infty,WO)\): For  every set \(M\) of well orderable sets such that for all \(x\in X\), \(|x|\ge 1\), there is a function \(f\) such that for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\).  (See Form 67.)

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 \(x\).

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