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Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic, 2022
Boolean algebra, named after the 19th century mathematician and logician, George Boole, has contributed to many aspects of computer science and information science.
P. Laplante +11 more
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Boolean algebra, named after the 19th century mathematician and logician, George Boole, has contributed to many aspects of computer science and information science.
P. Laplante +11 more
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IEEE Transactions on Computers, 1980
Switching algebra is unable to represent the dynamic behavior of digital circuits. There are several known methods for modeling the dynamics of circuits, using either multivalued algebras or specialized operators. None of them preserves the framework of switching algebra; therefore, existing analysis and synthesis methods developed by switching theory ...
Leinwand, S., Lamdan, T.
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Switching algebra is unable to represent the dynamic behavior of digital circuits. There are several known methods for modeling the dynamics of circuits, using either multivalued algebras or specialized operators. None of them preserves the framework of switching algebra; therefore, existing analysis and synthesis methods developed by switching theory ...
Leinwand, S., Lamdan, T.
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Acta Mathematica Sinica, English Series, 2004
Let \(X\) be a Banach space. The classical Orlicz-Pettis theorem says that weak subseries convergence already implies subseries convergence. The authors use the term \(P(\mathbb N)\) is \(X\)-weakly summing to express that the conclusion of the Orlicz-Pettis theorem holds in \(X\) when subseries corresponding to all subsets of \(\mathbb N\) are ...
Aizpuru, Antonio +1 more
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Let \(X\) be a Banach space. The classical Orlicz-Pettis theorem says that weak subseries convergence already implies subseries convergence. The authors use the term \(P(\mathbb N)\) is \(X\)-weakly summing to express that the conclusion of the Orlicz-Pettis theorem holds in \(X\) when subseries corresponding to all subsets of \(\mathbb N\) are ...
Aizpuru, Antonio +1 more
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Piecewise Boolean Algebras and Their Domains
International Colloquium on Automata, Languages and Programming, 2014We 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 ...
C. Heunen
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Algebraic partial Boolean algebras
Journal of Physics A: Mathematical and General, 2003Partial Boolean algebras are algebraic in this paper in the sense that their elements have coordinates in an algebraic number field. Within this context the author shows that every algebraic finitely-generated partial Boolean algebra is finite when the underlying space is three-dimensional.
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Mathematics of the USSR-Sbornik, 1973
The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras.
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The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras.
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2018
Boolean algebra, or the algebra of logic, was devised by the English mathematician George Boole (1815–64) and embodies the first successful application of algebraic methods to logic. Boole seems to have had several interpretations for his system in mind.
Sergei Kurgalin, Sergei Borzunov
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Boolean algebra, or the algebra of logic, was devised by the English mathematician George Boole (1815–64) and embodies the first successful application of algebraic methods to logic. Boole seems to have had several interpretations for his system in mind.
Sergei Kurgalin, Sergei Borzunov
+4 more sources
Boolean sets, skew Boolean algebras and a non-commutative Stone duality
, 2013We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and étalé spaces over Boolean spaces.
G. Kudryavtseva, M. Lawson
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Bi-Boolean Independence for Pairs of Algebras
, 2017In this paper, the notion of bi-Boolean independence for non-unital pairs of algebras is introduced thereby extending the notion of Boolean independence to pairs of algebras.
Yinzheng Gu, P. Skoufranis
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