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We have the following indirect implication of form equivalence classes:

181 \(\Rightarrow\) 282 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
181 \(\Rightarrow\) 8	clear
8 \(\Rightarrow\) 282	Infinite exponent partition relations and well-ordered choice, Kleinberg, E.M. 1973, J. Symbolic Logic note-97

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

Howard-Rubin Number	Statement
181:	\(C(2^{\aleph_0},\infty)\): Every set \(X\) of non-empty sets such that \(|X|=2^{\aleph_0}\) has a choice function.
8:	\(C(\aleph_{0},\infty)\):
282:	\(\omega\not\to(\omega)^{\omega}\).

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