A set-theoretic property called Property S is introduced as a generalization of the well-known Property B. Property S is named for A.Schrijver who first used it to formulate an equivalent of the boolean prime ideal theorem. It was independently introduced by A. Kolany to give a uniform treatment for a variety of satisfiability problems who then used a generalized resolution method to determine satisfiability. Here we further investigate Property S and the resolution method.
A Characterization of the Boolean Prime Ideal Theorem in Terms of Forcing Notions
Enrichments of Boolean Algebras: a uniform treatment of some classical and some novel examples
The independence of Stone's Theorem from the Boolean Prime Ideal Theorem
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