Implications

We have the following indirect implication of form equivalence classes:

40 \(\Rightarrow\) 324
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
40 \(\Rightarrow\) 165 clear
165 \(\Rightarrow\) 324 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.

165:

\(C(WO,WO)\):  Every well ordered family of non-empty, well orderable sets has a choice function.

324:

\(KW(WO,WO)\), The Kinna-Wagner Selection Principle for a well ordered family of well orderable sets: For every well ordered set \(M\) of well orderable sets, there is a function \(f\) such that for all \(A\in M\), if \(|A| > 1\) then \(\emptyset\neq f(A)\subsetneq A\). (See Form 15.)

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