Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
202 \(\Rightarrow\) 40 clear
40 \(\Rightarrow\) 86-alpha clear

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

Howard-Rubin Number Statement
202:

\(C(LO,\infty)\): Every linearly ordered family of non-empty sets has  a choice function.

40:

\(C(WO,\infty)\):  Every well orderable set of non-empty sets has a choice function. Moore, G. [1982], p 325.

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.

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