Axiom Of Choice

We have the following indirect implication of form equivalence classes:

86-alpha \(\Rightarrow\) 361 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
86-alpha \(\Rightarrow\) 8	clear
8 \(\Rightarrow\) 361	Zermelo's Axiom of Choice, Moore, 1982, page 325

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

Howard-Rubin Number	Statement
86-alpha:	\(C(\aleph_{\alpha},\infty)\): If \(X\) is a set of non-empty sets such that \(\|X\| = \aleph_{\alpha }\), then \(X\) has a choice function.
8:	\(C(\aleph_{0},\infty)\):
361:	In \(\Bbb R\), the union of a denumerable number of analytic sets is analytic. G. Moore [1982], pp 181 and 325.

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