On the Deductive Strength of Various Distributivity Axioms for Boolean Algebras in Set Theory

Mathematical Logic Quarterly 48 (3):413-426 (2002)
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Abstract

In this article, we shall show the generalized notions of distributivity of Boolean algebras have essential relations with several axioms and properties of set theory, say the Axiom of Choice, the Axiom of Dependence Choice, the Prime Ideal Theorems, Martin's axioms, Lebesgue measurability and so on

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Finiteness conditions and distributive laws for Boolean algebras.Marcel Erné - 2009 - Mathematical Logic Quarterly 55 (6):572-586.

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References found in this work

Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
On Ramsey's theorem and the axiom of choice.Gabriele Lolli - 1977 - Notre Dame Journal of Formal Logic 18 (4):599-601.
On a generalization of distributivity.Yasuo Kanai - 1994 - Journal of Symbolic Logic 59 (3):1055-1067.

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