Axiom Of Choice

We have the following indirect implication of form equivalence classes:

326 \(\Rightarrow\) 142 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
326 \(\Rightarrow\) 88	Logic at Work: Essay Dedicated to the Memory of Helen Rasiowa, Wojtylak, 1999,
88 \(\Rightarrow\) 142	The Axiom of Choice, Jech, 1973b, page 7 problem 11

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

Howard-Rubin Number	Statement
326:	2-SAT: Restricted Compactness Theorem for Propositional Logic III: If \(\Sigma\) is a set of formulas in a propositional language such that every finite subset of \(\Sigma\) is satisfiable and if every formula in \(\Sigma\) is a disjunction of at most two literals, then \(\Sigma\) is satisfiable. (A literal is a propositional variable or its negation.) Wojtylak [1999] (listed as Wojtylak [1995])
88:	\(C(\infty ,2)\): Every family of pairs has a choice function.
142:	\(\neg PB\): There is a set of reals without the property of Baire. Jech [1973b], p. 7.

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