Implications

We have the following indirect implication of form equivalence classes:

121 \(\Rightarrow\) 80
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
121 \(\Rightarrow\) 122 clear
122 \(\Rightarrow\) 80 clear

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

Howard-Rubin Number Statement
121:

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

122:

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

80:

\(C(\aleph_{0},2)\):  Every denumerable set of  pairs has  a  choice function.

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