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On the Deductive Strength of Various Distributivity Axioms for Boolean Algebras in Set Theory
Mathematical Logic Quarterly 48 (3):413-426 (2002)
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 onAuthor's Profile
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Citations of this work
Finiteness conditions and distributive laws for Boolean algebras.Marcel Erné - 2009 - Mathematical Logic Quarterly 55 (6):572-586.
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 the role of the baire category theorem and dependent choice in the foundations of logic.Robert Goldblatt - 1985 - Journal of Symbolic Logic 50 (2):412-422.
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.
The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice.Paul Howard & Jean E. Rubin - 1996 - Mathematical Logic Quarterly 42 (1):410-420.
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