Axiom Of Choice

We have the following indirect implication of form equivalence classes:

122 \(\Rightarrow\) 358 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
122 \(\Rightarrow\) 10	clear
10 \(\Rightarrow\) 358	clear

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

Howard-Rubin Number	Statement
122:	\(C(WO,<\aleph_{0})\): Every well ordered set of non-empty finite sets has a choice function.
10:	\(C(\aleph_{0},< \aleph_{0})\): Every denumerable family of non-empty finite sets has a choice function.
358:	\(KW(\aleph_0,<\aleph_0)\), The Kinna-Wagner Selection Principle for a denumerable family of finite sets: For every denumerable set \(M\) of finite sets there is a function \(f\) such that for all \(A\in M\), if \(\|A\| > 1\) then \(\emptyset\neq f(A)\subsetneq A\).

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