Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 199(\(n\))
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 199(\(n\))

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.

199(\(n\)):

(For \(n\in\omega-\{0,1\}\)) If all \(\varSigma^{1}_{n}\), Dedekind finite subsets of \({}^{\omega }\omega\) are finite, then all \(\varPi^1_n\) Dedekind finite subsets of \({}^{\omega} \omega\) are finite.

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