Implications

We have the following indirect implication of form equivalence classes:

393 \(\Rightarrow\) 250
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
393 \(\Rightarrow\) 121 clear
121 \(\Rightarrow\) 122 clear
122 \(\Rightarrow\) 250 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.

122:

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

250:

\((\forall n\in\omega-\{0,1\})(C(WO,n))\): For every natural number \(n\ge 2\), every well ordered family of \(n\) element sets has a choice function.

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