Implications

We have the following indirect implication of form equivalence classes:

106 \(\Rightarrow\) 185
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
106 \(\Rightarrow\) 126 Injectivity, projectivity and the axiom of choice, Blass, A. 1979, Trans. Amer. Math. Soc.
126 \(\Rightarrow\) 185 note-76

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

Howard-Rubin Number Statement
106:

Baire Category Theorem for Compact Hausdorff Spaces: Every compact Hausdorff space is Baire.

126:

\(MC(\aleph_0,\infty)\), Countable axiom of multiple choice: For every denumerable set \(X\) of non-empty sets there is a function \(f\) such that for all \(y\in X\), \(f(y)\) is a non-empty finite subset of \(y\).

185:

Every linearly ordered Dedekind finite set is finite.

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