Implications

We have the following indirect implication of form equivalence classes:

40 \(\Rightarrow\) 92
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
40 \(\Rightarrow\) 337 clear
337 \(\Rightarrow\) 92 clear

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

Howard-Rubin Number Statement
40:

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

337:

\(C(WO\), uniformly linearly ordered):  If \(X\) is a well ordered collection of non-empty sets and there is a function \(f\) defined on \(X\) such that for every \(x\in X\), \(f(x)\) is a linear ordering of \(x\), then there is a choice function for \(X\).

92:

\(C(WO,{\Bbb R})\):  Every well ordered family of non-empty subsets of \({\Bbb R}\) has a choice function.

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