Implications

We have the following indirect implication of form equivalence classes:

181 \(\Rightarrow\) 126
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
181 \(\Rightarrow\) 8 clear
8 \(\Rightarrow\) 126 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:

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

126:

\(MC(\aleph_0,\infty)\), Countable axiom of multiple choice: For every denumerable set \(X\) of non-empty sets there is a function \(f\) such that for all \(y\in X\), \(f(y)\) is a non-empty finite subset of \(y\).

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