Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
39 \(\Rightarrow\) 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
39:

\(C(\aleph_{1},\infty)\): Every set \(A\) of non-empty sets such that \(\vert A\vert = \aleph_{1}\) has a choice function. Moore, G. [1982], p. 202.

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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