Displaying similar documents to “Boolean algebras, splitting theorems, and Δ 2 0 sets”

Generalised irredundance in graphs: Nordhaus-Gaddum bounds

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 Ω f ( G ) . Only 64 Boolean functions f can produce different classes Ω f ( G ) , special cases...

The lattice of subvarieties of the biregularization of the variety of Boolean algebras

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 V b 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 τ b : + , · , ´ N , where...

FKN Theorem on the biased cube

Piotr Nayar (2014)

Colloquium Mathematicae

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We consider Boolean functions defined on the discrete cube - γ , γ - 1 equipped with a product probability measure μ n , where μ = β δ - γ + α δ γ - 1 and γ = √(α/β). This normalization ensures that the coordinate functions ( x i ) i = 1 , . . . , n are orthonormal in L ( - γ , γ - 1 , μ n ) . 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,...

On K -Boolean Rings

W. B. Vasantha Kandasamy (1992)

Publications du Département de mathématiques (Lyon)

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The rings which are Boolean

Ivan Chajda, Filip Švrček (2011)

Discussiones Mathematicae - General Algebra and Applications

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We study unitary rings of characteristic 2 satisfying identity x p = x 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 p = 2 n - 2 or p = 2 n - 5 or p = 2 n + 1 for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form 2 q + 2 m + 1 or 2 q + 2 m where q is a natural number and m 1 , 2 , . . . , 2 q - 1 .

A generalization of a formalized theory of fields of sets on non-classical logics

Helena Rasiowa

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Contents Introduction.................................................................................................................................................. 3 § 1. System 𝒮 of a propositional calculus...................................................................... 4 § 2. System 𝒮 * ..................................................................................................................... 5 § 3. 𝒮 * -algebras.....................................................................................................................

Laslett’s transform for the Boolean model in d

Rostislav Černý (2006)

Kybernetika

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Consider a stationary Boolean model X with convex grains in d and let any exposed lower tangent point of X be shifted towards the hyperplane N 0 = { x d : x 1 = 0 } by the length of the part of the segment between the point and its projection onto the N 0 covered by X . The resulting point process in the halfspace (the Laslett’s transform of X ) 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...

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a coherent P -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a P -point on ω , and show that these ultrafilters exist generically under 𝔠 = 𝔡 . This improves the known existence result of Ketonen [On the existence of P -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,...

Cardinal sequences of length < ω₂ under GCH

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 λ ( α ) = s ( α ) : s ( 0 ) = λ = m i n [ s ( β ) : β < α ] . We show that f ∈ (α) iff for some natural number n there are infinite cardinals λ i > λ > . . . > λ n - 1 and ordinals α , . . . , α n - 1 such that α = α + + α n - 1 and f = f f . . . f n - 1 where each f i λ i ( α i ) . Under GCH we prove that if α < ω₂ then (i) ω ( α ) = s α ω , ω : s ( 0 ) = ω ; (ii) if λ > cf(λ) = ω, λ ( α ) = s α λ , λ : s ( 0 ) = λ , s - 1 λ i s ω - c l o s e d i n α ; (iii) if cf(λ) = ω₁, λ ( α ) = s α λ , λ : s ( 0 ) = λ , s - 1 λ i s ω - c l o s e d a n d s u c c e s s o r - c l o s e d i n α ; (iv) if cf(λ) > ω₁, λ ( α ) = α λ . This yields a complete characterization of the classes (α) for all...

A representation theorem for tense n × m -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced n × m -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of n -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class n × m of tense n × m -valued Łukasiewicz-Moisil algebras (or tense LM n × m -algebras), namely n × m -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras

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 c the variety of type τ defined by all clone compatible identities from Id(). We call c the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of c , where is the...