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On the Deductive Strength of Various Distributivity Axioms for Boolean Algebras in Set Theory
Author(s) -
Kanai Yasuo
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200204)48:3<413::aid-malq413>3.0.co;2-c
Subject(s) - distributivity , mathematics , axiom , axiom of choice , zermelo–fraenkel set theory , constructive set theory , urelement , stone's representation theorem for boolean algebras , ideal (ethics) , set (abstract data type) , discrete mathematics , algebra over a field , set theory , pure mathematics , two element boolean algebra , epistemology , distributive property , computer science , philosophy , geometry , filtered algebra , programming language
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.