Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 270
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 270

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

Howard-Rubin Number Statement
1:

\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

270:

\(CT_{\hbox{fin}}\): The compactness theorem for propositional logic restricted to sets of formulas in which each variable occurs only in a finite number of formulas.

Comment:

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