Implications

We have the following indirect implication of form equivalence classes:

306 \(\Rightarrow\) 93
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
306 \(\Rightarrow\) 93 L’axiome de M. Zermelo et son rˆole dans la th´eorie des ensembles et l’analyse, Sierpi'nski, W. 1918, Bull. Int. Acad. Sci. Cracovie Cl. Math. Nat.

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

Howard-Rubin Number Statement
306:

The set of Vitali equivalence classes is linearly orderable. (Vitali equivalence classes are equivalence classes of the real numbers under the relation \(x\equiv y\leftrightarrow (\exists q\in{\Bbb Q})(x-y = q)\).).

93:

There is a non-measurable subset of \({\Bbb R}\).

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