-theories of Boolean algebras
Jan Waszkiewicz (1974)
Colloquium Mathematicae
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Jan Waszkiewicz (1974)
Colloquium Mathematicae
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Ernest J. Cockayne, Stephen Finbow (2004)
Discussiones Mathematicae Graph Theory
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For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by . Only 64 Boolean functions f can produce different classes , special cases...
Jerzy Płonka (2001)
Discussiones Mathematicae - General Algebra and Applications
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Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type , where...
Leila Fazlpar, Ali Armandnejad (2023)
Czechoslovak Mathematical Journal
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Let be an matrix of zeros and ones. The matrix is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero -entry. We characterize all linear maps perserving the set of Ferrers vectors over the binary Boolean semiring and over the Boolean ring . Also, we have achieved the number of these linear maps in each case.
Piotr Nayar (2014)
Colloquium Mathematicae
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We consider Boolean functions defined on the discrete cube equipped with a product probability measure , where and γ = √(α/β). This normalization ensures that the coordinate functions are orthonormal in . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover,...
W. B. Vasantha Kandasamy (1992)
Publications du Département de mathématiques (Lyon)
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Ivan Chajda, Filip Švrček (2011)
Discussiones Mathematicae - General Algebra and Applications
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We study unitary rings of characteristic 2 satisfying identity for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if or or for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form or where q is a natural number and .
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Helena Rasiowa
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Contents Introduction.................................................................................................................................................. 3 § 1. System of a propositional calculus...................................................................... 4 § 2. System ..................................................................................................................... 5 § 3. -algebras.....................................................................................................................
Rostislav Černý (2006)
Kybernetika
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Consider a stationary Boolean model with convex grains in and let any exposed lower tangent point of be shifted towards the hyperplane by the length of the part of the segment between the point and its projection onto the covered by . The resulting point process in the halfspace (the Laslett’s transform of ) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie...
Jan Starý (2015)
Commentationes Mathematicae Universitatis Carolinae
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We introduce the notion of a coherent -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a -point on , and show that these ultrafilters exist generically under . This improves the known existence result of Ketonen [On the existence of -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1,...
Jan Waszkiewicz (1973)
Colloquium Mathematicae
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István Juhász, Lajos Soukup, William Weiss (2006)
Fundamenta Mathematicae
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Let (α) denote the class of all cardinal sequences of length α associated with compact scattered spaces (or equivalently, superatomic Boolean algebras). Also put . We show that f ∈ (α) iff for some natural number n there are infinite cardinals and ordinals such that and where each . Under GCH we prove that if α < ω₂ then (i) ; (ii) if λ > cf(λ) = ω, ; (iii) if cf(λ) = ω₁, ; (iv) if cf(λ) > ω₁, . This yields a complete characterization of the classes (α) for all...
Andrey Krutov, Pavle Pandžić (2024)
Archivum Mathematicum
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We propose a definition of a quantised -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of are natural examples of such algebras.