A remark on $\lambda $-regular orthomodular lattices

Vladimír Rogalewicz

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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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On the structure of numerical event spaces

Gerhard Dorfer, Dietmar W. Dorninger, Helmut Länger (2010)

Kybernetika

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The probability $p (s)$ of the occurrence of an event pertaining to a physical system which is observed in different states $s$ determines a function $p$ from the set $S$ of states of the system to $[0, 1]$ . The function $p$ is called a numerical event or multidimensional probability. When appropriately structured, sets $P$ of numerical events form so-called algebras of $S$ -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions $p$ with an inherent full set of states....

A note on weakly $𝔪$ -distributive Boolean algebras

R. H. Lagrange (1970)

Colloquium Mathematicae

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On BPI Restricted to Boolean Algebras of Size Continuum

Eric Hall, Kyriakos Keremedis (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product $2^{(ω)}$ the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of $2^{(ω)}$ to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean...

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

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This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice $L_{C V} (K)$ of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a $P_{κ}$ -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras,...

Egoroff, σ, and convergence properties in some archimedean vector lattices

A. W. Hager, J. van Mill (2015)

Studia Mathematica

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An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each ${a ₙ}_{n \in ℕ} c o n A ⁺$ there are ${λ ₙ}_{n \in ℕ} \subseteq (0, \infty)$ and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent,...

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

Michael Morley, Robert Soare (1975)

Fundamenta Mathematicae

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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...

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

Jan Waszkiewicz (1974)

Colloquium Mathematicae

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Displaying similar documents to “A remark on $λ$ -regular orthomodular lattices”