Axiom Of Choice

We have the following indirect implication of form equivalence classes:

147 \(\Rightarrow\) 145 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
147 \(\Rightarrow\) 91	The axiom of choice in topology, Brunner, N. 1983d, Notre Dame J. Formal Logic note-26
91 \(\Rightarrow\) 145	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
147:	\(A(D2)\): Every \(T_2\) topological space \((X,T)\) can be covered by a well ordered family of discrete sets.
91:	\(PW\): The power set of a well ordered set can be well ordered.
145:	Compact \(P_0\)-spaces are Dedekind finite. (A \(P_0\)-space is a topological space in which the intersection of a countable collection of open sets is open.)

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