Implications

We have the following indirect implication of form equivalence classes:

392 \(\Rightarrow\) 396
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
392 \(\Rightarrow\) 393 clear
393 \(\Rightarrow\) 396 clear

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

Howard-Rubin Number Statement
392:

\(C(LO,LO)\): Every linearly ordered set of linearly orderable sets has a choice function.

393:

\(C(LO,WO)\): Every linearly ordered set of non-empty well orderable sets has a choice function.

396:

\(MC(LO,WO)\): For each linearly ordered family of non-empty well orderable sets \(X\), there is a function \(f\) such that for all \(x\in X\) \(f(x)\) is a non-empty, finite subset of \(x\).

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