Implications

We have the following indirect implication of form equivalence classes:

286 \(\Rightarrow\) 322
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
286 \(\Rightarrow\) 40 S´eminaire d’Analyse 1992, Morillon, 1991b,
40 \(\Rightarrow\) 322 clear

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

Howard-Rubin Number Statement
286:

Extended Krein-Milman Theorem:  Let K be a quasicompact (sometimes called convex-compact), convex subset of a locally convex topological vector space, then K has an extreme point. H. Rubin/J. Rubin [1985], p. 177-178.

40:

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

322:

\(KW(WO,\infty)\), The Kinna-Wagner Selection Principle for a well ordered family of sets: For every  well ordered set \(M\) 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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