Implications

We have the following indirect implication of form equivalence classes:

219 \(\Rightarrow\) 219
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
219 \(\Rightarrow\) 219

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

Howard-Rubin Number Statement
219:

\((\forall n\in\omega-\{0\}) MC(\infty,WO\), relatively prime to \(n\)): For all non-zero \(n\in \omega\), if \(X\) is a set of non-empty well orderable sets, then there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a non-empty, finite subset of \(x\), and \(|f(x)|\) is relatively prime to \(n\).

219:

\((\forall n\in\omega-\{0\}) MC(\infty,WO\), relatively prime to \(n\)): For all non-zero \(n\in \omega\), if \(X\) is a set of non-empty well orderable sets, then there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a non-empty, finite subset of \(x\), and \(|f(x)|\) is relatively prime to \(n\).

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