-theories of Boolean algebras
Jan Waszkiewicz (1974)
Colloquium Mathematicae
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Jan Waszkiewicz (1974)
Colloquium Mathematicae
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Michael Morley, Robert Soare (1975)
Fundamenta Mathematicae
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Jerzy Płonka (2008)
Colloquium Mathematicae
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Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by the variety of type τ defined by all clone compatible identities from Id(). We call the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of , where is the...
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...
Ivan Chajda, Helmut Länger (2022)
Mathematica Bohemica
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We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular....
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.
Helena Rasiowa
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Contents Introduction.................................................................................................................................................. 3 § 1. System of a propositional calculus...................................................................... 4 § 2. System ..................................................................................................................... 5 § 3. -algebras.....................................................................................................................
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,...
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 .
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,...
Claude Tardif (2022)
Commentationes Mathematicae Universitatis Carolinae
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We prove that for any , there exists an infinite family of graphs such that for all and for all . These counterexamples to Hedetniemi’s conjecture show that the Boolean lattice of exponential graphs with as a base is infinite for .
Erhard Aichinger, Peter Mayr, R. McKenzie (2014)
Journal of the European Mathematical Society
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We prove that every clone of operations on a finite set , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting for some finitary relation over . It follows that for a fixed finite set , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...
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...
Mario Petrich (2020)
Mathematica Bohemica
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Completely regular semigroups are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes a variety; its lattice of subvarieties is denoted by . We study here the relations and relative to a sublattice of constructed in a previous publication. For being any of these relations, we determine the -classes of all varieties in the lattice as well as the restrictions of to .
Lidija Goračinova-Ilieva, Smile Markovski (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a positive integer. An algebra is said to have the property if all of its subalgebras generated by two distinct elements have exactly elements. A variety of algebras is a variety with the property if every member of has the property . Such varieties exist only in the case of prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property , , blocks of Steiner system of type are obtained. The stated correspondence...