Implications

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We have the following indirect implication of form equivalence classes:

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

Implication	Reference
113 \(\Rightarrow\) 8	Tychonoff's theorem implies AC, Kelley, J.L. 1950, Fund. Math. Products of compact spaces in the least permutation model, Brunner, N. 1985a, Z. Math. Logik Grundlagen Math.
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
113:	Tychonoff's Compactness Theorem for Countably Many Spaces: The product of a countable set of compact spaces is compact.
8:	\(C(\aleph_{0},\infty)\):
282:	\(\omega\not\to(\omega)^{\omega}\).

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