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Orthomodular Lattices Admitting No States
The purpose of this paper is to construct a class of orthomodular lattices which admit no bounded measures.
Sequential products on effect algebras
Abstract A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effectExpand
Filters and supports in orthoalgebras
An orthoalgebra, which is a natural generalization of an orthomodular lattice or poset, may be viewed as a “logic” or “proposition system” and, under a welldefined set of circumstances, its elementsExpand
On the structure of orthomodular lattices satisfying the chain condition
Abstract Beginning with the external point of view we show how orthomodular lattices may be “pasted” together to yield a new orthomodular lattice. Changing to the internal point of view we show thatExpand
Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics
List of Figures. List of Tables. Preface. Acknowledgements. I: Mathematical and Physical Background. Introduction. 1. The mathematical scenario of quantum theory and von Neumann's axiomatization.Expand
A Non-Standard Quantum Logic with a Strong Set of States
Since the discovery of non-Euclidian geometries the academic community has widely recognized the importance of non-standard models of axiomatic systems. This paper presents a non-standard quantumExpand
On Residuated Approximations
Commutator-finite orthomodular lattices
AbstractThe class $$\mathfrak{C}$$ of orthomodular lattices which have only finitely many commutators is investigated. The following theorems are proved: $$\mathfrak{C}$$ contains theExpand