Orthomodular lattices that are  horizontal sums of Boolean algebras

Ivan Chajda; Helmut Länger

Displaying similar documents to “Orthomodular lattices that are horizontal sums of Boolean algebras”

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 $τ_{b} : +, \cdot, ´ \to N$ , where...

Boolean algebras, splitting theorems, and $Δ_{2}^{0}$ sets

Michael Morley, Robert Soare (1975)

Fundamenta Mathematicae

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$\forall_{n}$ -theories of Boolean algebras

Jan Waszkiewicz (1974)

Colloquium Mathematicae

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A note on weakly $𝔪$ -distributive Boolean algebras

R. H. Lagrange (1970)

Colloquium Mathematicae

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On interval homogeneous orthomodular lattices

Anna de Simone, Mirko Navara, Pavel Pták (2001)

Commentationes Mathematicae Universitatis Carolinae

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An orthomodular lattice $L$ is said to be interval homogeneous (resp. centrally interval homogeneous) if it is $σ$ -complete and satisfies the following property: Whenever $L$ is isomorphic to an interval, $[a, b]$ , in $L$ then $L$ is isomorphic to each interval $[c, d]$ with $c \leq a$ and $d \geq b$ (resp. the same condition as above only under the assumption that all elements $a$ , $b$ , $c$ , $d$ are central in $L$ ). Let us denote by Inthom (resp. Inthom $_{c}$ ) the class of all interval homogeneous orthomodular lattices (resp. centrally interval...

On interval homogeneous orthomodular lattices

Anna de Simone, Mirko Navara, Pavel Pták (2001)

Commentationes Mathematicae Universitatis Carolinae

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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...

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...

FKN Theorem on the biased cube

Piotr Nayar (2014)

Colloquium Mathematicae

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We consider Boolean functions defined on the discrete cube $- γ, γ^{- 1} ⁿ$ equipped with a product probability measure $μ^{\otimes n}$ , 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 $L ₂ (- γ, γ^{- 1} ⁿ, μ^{\otimes n})$ . 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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Laslett’s transform for the Boolean model in $ℝ^{d}$

Rostislav Černý (2006)

Kybernetika

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Consider a stationary Boolean model $X$ with convex grains in $ℝ^{d}$ and let any exposed lower tangent point of $X$ be shifted towards the hyperplane $N_{0} = {x \in ℝ^{d} : x_{1} = 0}$ 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...

Linear preserver of $n \times 1$ Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

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Let $A = {[a_{i j}]}_{m \times n}$ be an $m \times n$ matrix of zeros and ones. The matrix $A$ is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero $(1, 1)$ -entry. We characterize all linear maps perserving the set of $n \times 1$ Ferrers vectors over the binary Boolean semiring and over the Boolean ring $ℤ_{2}$ . Also, we have achieved the number of these linear maps in each case.

Generalized $P_{0}$ -lattices of order ω+

T. Traczyk, W. Zarębski (1976)

Colloquium Mathematicae

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