Filters and supports in orthoalgebras

DOI10.1007/BF00678545zbMath0764.03026OpenAlexW1969490642MaRDI QIDQ1200425

Richard J. Greechie, Gottfried T. Rüttimann, David J. Foulis

Publication date: 16 January 1993

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00678545

zbMATH Keywords

orthomodular latticeorthoalgebracompactness theoremAristotelian modalitieslocal filtersproposition system

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Complemented lattices, orthocomplemented lattices and posets (06C15) Quantum logic (03G12)

Related Items (88)

Empirical logics ⋮ Counterexamples in difference posets and orthoalgebras ⋮ Difference posets, effects, and quantum measurements ⋮ Logicoalgebraic structures. II: Supports in test spaces ⋮ Quotients of interval effect algebras ⋮ Conjunctions, disjunctions, and Bell-type inequalities in orthoalgebras ⋮ Product of partition logics, orthoalgebras, and automata ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Decompositions of measures on orthoalgebras and difference posets ⋮ Test spaces, Dacey spaces, and completeness of inner product spaces ⋮ Unitizations of generalized pseudo effect algebras and their ideals ⋮ Difference posets and the histories approach to quantum theories ⋮ Orthosummable orthoalgebras ⋮ Extensions of real-valued difference posets ⋮ Sums and products of interval algebras ⋮ Musings about the triple representation theorem for effect algebras ⋮ Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property ⋮ Unnamed Item ⋮ The logics of orthoalgebras ⋮ Noncommutative version of Nikodym boundedness theorem for uniform space- valued functions ⋮ Unnamed Item ⋮ Topos theory and consistent histories: The internal logic of the set of all consistent sets ⋮ D-lattices ⋮ Tensor product of difference posets and effect algebras ⋮ Transition to effect algebras ⋮ States on orthoalgebras ⋮ Strong law of large numbers in D-posets ⋮ Compatibility in D-posets ⋮ Partial Abelian semigroups ⋮ Symmetry and topology in quantum logic ⋮ Unnamed Item ⋮ Compatibility of observables on effect algebras ⋮ The center of an effect algebra ⋮ Test groups and effect algebras ⋮ Semi-orthoposets ⋮ Quantum MV algebras ⋮ Event structures in nonstandard quantum mechanics ⋮ The classification of decoherence functionals: An analog of Gleason’s theorem ⋮ Generalized ideals and supports in pseudo effect algebras ⋮ The structure group of a non-degenerate effect algebra ⋮ A unified framework for the algebra of unsharp quantum mechanics ⋮ Common generalizations of orthocomplete and lattice effect algebras ⋮ States as morphisms ⋮ Quantum observable generalized orthoalgebras ⋮ Triple representation theorem for orthocomplete homogeneous effect algebras ⋮ The intersection operation in light of joint observables and Bell inequalities in operational probability theory ⋮ Notes on sharp and principal elements in effect algebras ⋮ Covariance and quantum logic ⋮ Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory ⋮ Continuous histories and the history group in generalized quantum theory ⋮ Stateless quantum structures and extremal graph theory ⋮ A note of filters in effect algebras. ⋮ The center of a generalized effect algebra. ⋮ Quotients of dimension effect algebras ⋮ An intrinsic topology for orthomodular lattices ⋮ Convergence theorems for topological group valued measures on effect algebras ⋮ Centrally orthocomplete effect algebras ⋮ Type-decomposition of an effect algebra ⋮ A combinatorial approach to nonlocality and contextuality ⋮ Effect algebras and unsharp quantum logics. ⋮ Partial and unsharp quantum logics. ⋮ Indeterministic objects in the category of effect algebras and the passage to the semiclassical limit ⋮ Pseudo difference posets and pseudo Boolean D-posets ⋮ Sharp and meager elements in orthocomplete homogeneous effect algebras ⋮ Top element problem and MacNeille completions of generalized effect algebras ⋮ Boolean subalgebras of orthoalgebras ⋮ Topological test spaces ⋮ Orthomodularity of decompositions in a categorical setting ⋮ Quantum observables and effect algebras ⋮ Effect algebras as presheaves on finite Boolean algebras ⋮ Pseudo effect algebras are algebras over bounded posets ⋮ Meager projections in orthocomplete homogeneous effect algebras ⋮ A link between quantum logic and categorical quantum mechanics ⋮ Unnamed Item ⋮ A non-commutative version of the first Alexandroff decomposition theorem in ordered topological groups ⋮ Unnamed Item ⋮ Effect algebras with the maximality property ⋮ Material implications in lattice effect algebras ⋮ Augmented temporal logic formalism for histories-based generalized quantum mechanics ⋮ On quantum vs. classical probability ⋮ Atomistic and orthoatomistic effect algebras ⋮ Atomic effect algebras with compression bases ⋮ New families of finite coherent orthoalgebras without bivaluations ⋮ Tensor products of orthoalgebras ⋮ \(\sigma\)-additivity in manuals and orthoalgebras ⋮ Unitizing a generalized pseudo effect algebra. ⋮ On the Extension of D-Poset Valued Measures

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• Banach spaces of weights on quasimanuals
• Connections among quantum logics. I: Quantum propositional logics
• Connections among quantum logics. II: Quantum event logics
• Tensor products and probability weights
• Realistic quantum probability
• Quantifiers and orthomodular lattices
• The Approximate Jordan-Hahn Decomposition
• Non-commutative spectral theory for affine function spaces on convex sets

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