Orthomodular lattices admitting no states
From MaRDI portal
Publication:2546886
DOI10.1016/0097-3165(71)90015-XzbMath0219.06007MaRDI QIDQ2546886
Publication date: 1971
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Enumerative combinatorics (05A99) Boolean algebras (Boolean rings) (06E99) Complemented lattices, orthocomplemented lattices and posets (06C15)
Related Items
Noncontextual coloring of orthogonality hypergraphs ⋮ Orthosystems of submodules of a module ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Finitary Imbeddings of Certain Generalized Sample Spaces ⋮ Unnamed Item ⋮ Orthomodular lattices with state-separated noncompatible pairs ⋮ Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces ⋮ Unnamed Item ⋮ Quantum measurements and quantum logics ⋮ Unnamed Item ⋮ A Theorem on Pure States on a Hypergraph ⋮ Unnamed Item ⋮ Lattices and Their Consistent Quantification ⋮ Maximum likelihood estimator of quantum probabilities ⋮ On blocks in the products and ultraproducts of orthomodular lattices ⋮ A symmetric-difference-closed orthomodular lattice that is stateless ⋮ Matrix representation of finite effect algebras ⋮ Generalized \(\mathbb{XOR}\) operation and the categorical equivalence of the abbott algebras and quantum logics ⋮ On locally finite orthomodular lattices ⋮ The stability of pure weights under conditioning ⋮ Effect algebras and statistical physical theories ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A remark on $\lambda$-regular orthomodular lattices ⋮ Yosida-Hewitt and Lebesgue decompositions of states on orthomodular posets ⋮ Unnamed Item ⋮ Unnamed Item ⋮ States and Boolean Algebra ⋮ Unnamed Item ⋮ Quantum Logics with Lattice State Spaces ⋮ Spaces of observables ⋮ Jauch–Piron states on quantum logics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Orthomodular lattices admitting no states ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Generalized monotone convergence and Radon–Nikodym theorems ⋮ Basic decomposition of elements and Jauch-Piron effect algebras ⋮ Measurements, Hilbert space and quantum logics ⋮ Weak dispersion-free states and the hidden variables hypothesis ⋮ Graph approach to quantum systems ⋮ Unnamed Item ⋮ Every Finite Group is the Automorphism Group of Some Finite Orthomodular Lattice ⋮ Operational Statistics. I. Basic Concepts ⋮ Logicoalgebraic structures. I ⋮ Empirical logics ⋮ Jauch-Piron property (everywhere!) in the logicoalgebraic foundation of quantum theories ⋮ Set logics and their representations ⋮ What does pasting manage in OMPs? ⋮ Continuous lattice effect algebras admitting order-continuous states ⋮ Logicoalgebraic structures. II: Supports in test spaces ⋮ Pasting of lattice-ordered effect algebras ⋮ Examples, problems, and results in effect algebras ⋮ Orthomodular lattices that are \(Z_2\)-rich ⋮ Partially additive measures and set representations of orthoposets ⋮ Equational bases for some varieties of orthomodular lattices related to states ⋮ Fuzzy quantum logics and infinite-valued Łukasiewicz logic ⋮ Copula and s-map on a quantum logic ⋮ Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property ⋮ On the interplay of the centre and the state space in quantum logics ⋮ Expected utility theory under non-classical uncertainty ⋮ Quantum logics with the Radon-Nikodym property ⋮ Automorphism groups and the full state spaces of the Petersen graph generalizations of \(G_{32}\) ⋮ Representative graphs of r-regular partial planes and representation of orthomodular posets ⋮ An introduction to lattice based probability theories ⋮ Faithful orthogonal representations of graphs from partition logics ⋮ Boolean quotients of orthomodular lattices ⋮ States on orthoalgebras ⋮ Operation associated to partitions and best extension of signed measures on set logics ⋮ Chain tensor products and interval effect algebras ⋮ Finite function spaces and measures on hypergraphs ⋮ On the range of non-classical probability ⋮ Positive sets in finite linear function spaces ⋮ Decompositions of supermodular functions and \(\square\)-decomposable measures ⋮ Spaces of abstract events ⋮ The structure group of a non-degenerate effect algebra ⋮ Characterization of spaces of filtering states ⋮ Marginality and triangle inequality ⋮ Automorphism groups of small \((3,3)\)-homogeneous logics ⋮ Embedding quantum logics in Hilbert space ⋮ Two-dimensional observables and spectral resolutions ⋮ Small quantum structures with small state spaces ⋮ Covariance and quantum logic ⋮ A \((3,3)\)-homogeneous quantum logic with 18 atoms. I ⋮ The inheritance of BDE-property in sharply dominating lattice effect algebras and \((o)\)-continuous states ⋮ Characterization of Boolean algebras in terms of certain states of Jauch-Piron type ⋮ There are loops of order three in orthomodular lattices ⋮ Stateless quantum structures and extremal graph theory ⋮ Kochen-Specker sets and generalized orthoarguesian equations ⋮ Constructive approach to logics of physical systems: Application to EPR case ⋮ Orthomodular posets related to \(Z_2\)-valued states ⋮ \(n\)-orthodistributivity in orthomodular lattices ⋮ Unscrambling the quantum omelette ⋮ Non-contextual chocolate balls versus value indefinite quantum cryptography ⋮ One-sided orthogonality, orthomodular spaces, quantum sets, and a class of Garside groups ⋮ Bibliography on quantum logics and related structures ⋮ Bell-type inequalities for bivariate maps on orthomodular lattices ⋮ States on sharply dominating effect algebras ⋮ On the representation of measures over bounded lattices ⋮ Quantum structures without group-valued measures ⋮ Quantum violation of the suppes-zanotti inequalities and ``contextuality ⋮ Hilbert-space-valued states on quantum logics ⋮ States and synaptic algebras ⋮ Generalised Kochen-Specker theorem in three dimensions ⋮ Varieties of orthocomplemented lattices induced by Łukasiewicz-groupoid-valued mappings ⋮ Orthoalgebras as pastings of Boolean algebras ⋮ A new axiomatization of unified quantum logic ⋮ Logic of likelihood ⋮ Independence of automorphism group, center, and state space of quantum logics ⋮ On the structure of pseudo BL-algebras and pseudo hoops in quantum logics ⋮ An orthomodular lattice ⋮ A combinatorial approach to nonlocality and contextuality ⋮ A characterization of state spaces of orthomodular lattices ⋮ Some results from the combinatorial approach to quantum logic ⋮ The pasting constructions of lattice ordered effect algebras ⋮ Empirical logic and quantum mechanics ⋮ A note on Jauch-Piron states ⋮ Maps on a quantum logic ⋮ Von Neumann algebras, \(L\)-algebras, Baer*-monoids, and Garside groups ⋮ States on orthomodular amalgamations over trees ⋮ Equations holding in Hilbert lattices ⋮ On Frink ideals in orthomodular posets ⋮ Existence of states on quantum structures ⋮ On extension of joint distribution functions on quantum logics ⋮ Orthocomplemented posets with a symmetric difference ⋮ A particular non-atomistic orthomodular poset ⋮ Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis ⋮ Quantum logics that are symmetric-difference-closed ⋮ The lattice and simplex structure of states on pseudo effect algebras ⋮ Lifting, \(n\)-dimensional spectral resolutions, and \(n\)-dimensional observables ⋮ Effect algebras with the maximality property ⋮ Measures on orthomodular partially ordered sets ⋮ Orthomodulare Verbände mit Regularitaetsbedingungen ⋮ An algebraic model of observable properties in distributed systems ⋮ Astroids and pastings ⋮ An orthomodular analogue of the Birkhoff-Menger theorem ⋮ Calculus for non-compatible observables, construction through conditional states ⋮ Small orthomodular partial algebras. ⋮ The Brooks-Jewett theorem on an orthomodular lattice ⋮ Varieties of orthomodular lattices related to states ⋮ Tensor products of orthoalgebras ⋮ Fractal properties of MV-algebra pastings. ⋮ Characterization of homogeneity in orthocomplete atomic effect algebras ⋮ Information-theoretic princple entails orthomodularity of a lattice
Cites Work
- Unnamed Item
- Unnamed Item
- Quantifiers and orthomodular lattices
- Hilbert space, independence, and generalized probability
- Orthomodular lattices admitting no states
- Atomic orthocomplemented lattices
- Probability in physics and a theorem on simultaneous observability
- On the structure of orthomodular lattices satisfying the chain condition
- Spectral Methods for a Generalized Probability Theory
- A Finite Orthomodular Lattice Which Does Not Admit a Full Set of States
- A Radon-Nikodym Theorem in Dimension Lattices
