Implications

We have the following indirect implication of form equivalence classes:

132 \(\Rightarrow\) 132
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
132 \(\Rightarrow\) 132 Ramsey's theorem in the hierarchy of choice principles, Blass, A. 1977a, J. Symbolic Logic
The independence of Ramsey's theorem, Kleinberg, E.M. 1969, J. Symbolic Logic

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

Howard-Rubin Number Statement
132:

\(PC(\infty, <\aleph_0,\infty)\):  Every infinite family of finite  sets has an infinite subfamily with a choice function.

132:

\(PC(\infty, <\aleph_0,\infty)\):  Every infinite family of finite  sets has an infinite subfamily with a choice function.

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