Implications

We have the following indirect implication of form equivalence classes:

181 \(\Rightarrow\) 16
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
181 \(\Rightarrow\) 8 clear
8 \(\Rightarrow\) 16 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:

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

16:

\(C(\aleph_{0},\le 2^{\aleph_{0}})\):  Every denumerable collection of non-empty sets  each with power \(\le  2^{\aleph_{0}}\) has a choice function.

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