Implications

We have the following indirect implication of form equivalence classes:

67 \(\Rightarrow\) 116
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
67 \(\Rightarrow\) 116 clear

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

Howard-Rubin Number Statement
67:

\(MC(\infty,\infty)\) \((MC)\), The Axiom of Multiple Choice: For every set \(M\) of non-empty sets there is a function \(f\) such that \((\forall x\in M)(\emptyset\neq f(x)\subseteq x\) and \(f(x)\) is finite).

116:

Every compact \(T_2\) space is weakly  Loeb. Weakly Loeb means the set of non-empty closed subsets has a multiple choice function.

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