Implications

We have the following indirect implication of form equivalence classes:

325 \(\Rightarrow\) 325
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
325 \(\Rightarrow\) 325

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

Howard-Rubin Number Statement
325:

Ramsey's Theorem II: \(\forall n,m\in\omega\), if A is an infinite set and the family of all \(m\) element subsets of \(A\) is partitioned into \(n\) sets \(S_{j}, 1\le j\le n\), then there is an infinite subset \(B\subseteq A\) such that all \(m\) element subsets of \(B\) belong to the same \(S_{j}\). (Also, see Form 17.)

325:

Ramsey's Theorem II: \(\forall n,m\in\omega\), if A is an infinite set and the family of all \(m\) element subsets of \(A\) is partitioned into \(n\) sets \(S_{j}, 1\le j\le n\), then there is an infinite subset \(B\subseteq A\) such that all \(m\) element subsets of \(B\) belong to the same \(S_{j}\). (Also, see Form 17.)

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