Implications

We have the following indirect implication of form equivalence classes:

62 \(\Rightarrow\) 285
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
62 \(\Rightarrow\) 285 On functions without fixed points, Wi'sniewski, K. 1973, Comment. Math. Prace Mat.

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

Howard-Rubin Number Statement
62:

\(C(\infty,< \aleph_{0})\):  Every set of non-empty finite  sets  has  a choice function.

285:

Let \(E\) be a set and \(f: E\to E\), then \(f\) has a fixed point if and only if \(E\) is not the union of three mutually disjoint sets \(E_1\), \(E_2\) and \(E_3\) such that \(E_i \cap f(E_i) = \emptyset\) for \(i=1, 2, 3\).

Comment:

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