Implications

We have the following indirect implication of form equivalence classes:

114 \(\Rightarrow\) 118
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
114 \(\Rightarrow\) 90 Products of compact spaces in the least permutation model, Brunner, N. 1985a, Z. Math. Logik Grundlagen Math.
90 \(\Rightarrow\) 118 Horrors of topology without AC: A non-normal orderable space, van Douwen, E.K. 1985, Proc. Amer. Math. Soc.

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

Howard-Rubin Number Statement
114:

Every A-bounded \(T_2\) topological space is weakly Loeb. (\(A\)-bounded means amorphous subsets are relatively compact. Weakly Loeb means the set of non-empty closed subsets has a multiple choice function.)

90:

\(LW\):  Every linearly ordered set can be well ordered. Jech [1973b], p 133.

118:

Every linearly orderable topological space is normal.  Birkhoff [1967], p 241.

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