Implications

We have the following indirect implication of form equivalence classes:

179-epsilon \(\Rightarrow\) 125
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
179-epsilon \(\Rightarrow\) 144 clear
144 \(\Rightarrow\) 125 P-Raüme and Auswahlaxiom, Brunner, N. 1984c, Rend. Circ. Mat. Palermo.

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.

125:

There does not exist an infinite, compact connected \(p\) space. (A \(p\) space is a \(T_2\) space in which the intersection of any well orderable family of open sets is open.)

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