Implications

We have the following indirect implication of form equivalence classes:

181 \(\Rightarrow\) 355
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
181 \(\Rightarrow\) 8 clear
8 \(\Rightarrow\) 355 clear

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

Howard-Rubin Number Statement
181:

\(C(2^{\aleph_0},\infty)\): Every set \(X\) of non-empty sets such that \(|X|=2^{\aleph_0}\) has a choice function.

8:

\(C(\aleph_{0},\infty)\):

355:

\(KW(\aleph_0,\infty)\), The Kinna-Wagner Selection Principle for a denumerable family of sets: For every denumerable set \(M\) there is a function \(f\) such that for all \(A\in M\), if \(|A| > 1\) then \(\emptyset\neq f(A)\subsetneq A\).

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