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BOOLEAN ALGEBRA Boolean algebra
"... or the algebra of logic, was devised by the English mathematician George Boole (181564), and embodies the first successful application of algebraic methods to logic. Boole seems initially to have conceived of each of the basic symbols of his algebraic system as standing for the mental operation of ..."
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) disjunction or (disjoint) union, and subtraction, corresponding to "excepting " or diifference. Boole's ideas as outlined here have since undergone extensive development, and the resulting mathematical concept of Boolean algebra now plays a central role in mathematical logic
A Plaidoyer for Boolean Algebra
, 2013
"... I propose that the basics of Boolean Algebra become a part of the standard Introduction to Proof course. ..."
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I propose that the basics of Boolean Algebra become a part of the standard Introduction to Proof course.
BOOLEAN ALGEBRA APPROXIMATIONS
, 2010
"... Knight and Stob proved that every low4 Boolean algebra is 0 (6)isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0 (n+2)isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0 (7)isomorph ..."
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Knight and Stob proved that every low4 Boolean algebra is 0 (6)isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0 (n+2)isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0 (7
Symmetric Boolean algebras
"... We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusionexclusion principle. ..."
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We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusionexclusion principle.
Rough operations on Boolean algebras
, 2004
"... In this paper, we introduce two pairs of rough operations on Boolean algebras. First we define a pair of rough approximations based on a partition of the unity of a Boolean algebra. We then propose a pair of generalized rough approximations on Boolean algebras after defining a basic assignment funct ..."
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In this paper, we introduce two pairs of rough operations on Boolean algebras. First we define a pair of rough approximations based on a partition of the unity of a Boolean algebra. We then propose a pair of generalized rough approximations on Boolean algebras after defining a basic assignment
Handbook of Boolean Algebras
, 1989
"... Abstract. We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semiCohen algebras, pseudoCohen alg ..."
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Abstract. We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semiCohen algebras, pseudo
Piecewise Boolean algebras and their domains
"... Abstract. We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise Boolean domains equipped with an orientation, or as ..."
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Abstract. We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise Boolean domains equipped with an orientation
BOOLEAN ALGEBRAS AND LOGIC
, 809
"... Abstract. In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will ..."
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Abstract. In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic
Simple complete Boolean algebras
 Israel J. Math
, 1974
"... Abstract. For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators. 694 revision:20040502 modified:20040502 1. Introduction. A complete Boolean algebra is simple if it is atomless and has no nontrivial proper atomless complete subalgebra. The problem of the e ..."
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Abstract. For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators. 694 revision:20040502 modified:20040502 1. Introduction. A complete Boolean algebra is simple if it is atomless and has no nontrivial proper atomless complete subalgebra. The problem
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