Axiom Of Choice

We have the following indirect implication of form equivalence classes:

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

Implication	Reference
90 \(\Rightarrow\) 91	The Axiom of Choice, Jech, 1973b, page 133
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
90:	\(LW\): Every linearly ordered set can be well ordered. Jech [1973b], p 133.
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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