Displaying similar documents to “On the structure of numerical event spaces”

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 ≤ a and d ≥ 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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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 ≤ a and d ≥ 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...

Ring-like structures derived from λ -lattices with antitone involutions

Ivan Chajda (2007)

Mathematica Bohemica

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Using the concept of the λ -lattice introduced recently by V. Snášel we define λ -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

A remark on λ -regular orthomodular lattices

Vladimír Rogalewicz (1989)

Aplikace matematiky

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A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality k is called λ -regular, if each atom is a member of just λ blocks. We estimate the minimal number of blocks of λ -regular orthomodular lattices to be lower than of equal to λ 2 regardless of k .

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...

A measure-theoretic characterization of Boolean algebras among orthomodular lattices

Pavel Pták, Sylvia Pulmannová (1994)

Commentationes Mathematicae Universitatis Carolinae

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We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.