A New View of Effects in a Hilbert Space

Studia Logica 104 (6):1145-1177 (2016)
  Copy   BIBTEX

Abstract

We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of PBZ*-lattices and their reducts; in particular, we prove some embedding results for PBZ*-lattices and provide an initial description of the lattice of PBZ*-varieties.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,069

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A semantical investigation on Brouwer-Zadeh logic.Roberto Giuntini - 1991 - Journal of Philosophical Logic 20 (4):411 - 433.
Infinite substructure lattices of models of Peano Arithmetic.James H. Schmerl - 2010 - Journal of Symbolic Logic 75 (4):1366-1382.
Quantum logic revisited.L. Román & B. Rumbos - 1991 - Foundations of Physics 21 (6):727-734.
Complementarity in Categorical Quantum Mechanics.Chris Heunen - 2012 - Foundations of Physics 42 (7):856-873.
Type-Decomposition of an Effect Algebra.David J. Foulis & Sylvia Pulmannová - 2010 - Foundations of Physics 40 (9-10):1543-1565.
Splittings of lattices of quasivarieties.Andrzej Wronski - 1981 - Bulletin of the Section of Logic 10 (3):128-129.
Partial and unsharp quantum logics.M. L. Dalla Chiara & R. Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.

Analytics

Added to PP
2016-05-14

Downloads
32 (#445,919)

6 months
6 (#252,172)

Historical graph of downloads
How can I increase my downloads?

Author Profiles