Axiom Of Choice

We have the following indirect implication of form equivalence classes:

22 \(\Rightarrow\) 22 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
22 \(\Rightarrow\) 22	Le¸cons sur la th´eorie des fonctions, Borel, [1898] Zermelo's Axiom of Choice, Moore, [1982]

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

Howard-Rubin Number	Statement
22:	\(UT(2^{\aleph_{0}},2^{\aleph_{0}},2^{\aleph_{0}})\): If every member of an infinite set of cardinality \(2^{\aleph _{0}}\) has power \(2^{\aleph_{0}}\), then the union has power \(2^{\aleph_{0}}\).
22:	\(UT(2^{\aleph_{0}},2^{\aleph_{0}},2^{\aleph_{0}})\): If every member of an infinite set of cardinality \(2^{\aleph _{0}}\) has power \(2^{\aleph_{0}}\), then the union has power \(2^{\aleph_{0}}\).

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