Implications

We have the following indirect implication of form equivalence classes:

179-epsilon \(\Rightarrow\) 413
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
179-epsilon \(\Rightarrow\) 144 clear
144 \(\Rightarrow\) 413 Constructive order theory, Ern'e, M. 2001, Math. Logic Quart.

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

Howard-Rubin Number Statement
179-epsilon:

Suppose  \(\epsilon > 0\) is an ordinal. \(\forall x\), \(x\in W(\epsilon\)).

144:

Every set is almost well orderable.

413:

Every infinite set \(S\) is the union of a set, well-ordered by inclusion, of subsets which are non-equipollent to \(S\).  

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