Implications

We have the following indirect implication of form equivalence classes:

393 \(\Rightarrow\) 120-K
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
393 \(\Rightarrow\) 121 clear
121 \(\Rightarrow\) 120-K clear

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

Howard-Rubin Number Statement
393:

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

121:

\(C(LO,<\aleph_{0})\): Every linearly ordered set of non-empty finite sets has a choice function.

120-K:

If \(K\subseteq\omega-\{0,1\}\), \(C(LO,K)\): Every linearly ordered set of non-empty sets each of whose cardinality is in \(K\) has a choice function.

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