Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quantum logics with lattice state spaces


Authors: Jiří Binder and Mirko Navara
Journal: Proc. Amer. Math. Soc. 100 (1987), 688-693
MSC: Primary 81B10; Secondary 03G12, 06C15, 46L60
MathSciNet review: 894439
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ L$ be a quantum logic and let $ S(L)$ denote the set of all states on $ L$. (By a state we mean a nonnegative bounded $ \sigma $-additive measure, not necessarily normalized.) We ask whether every logic whose state space is a lattice has to be Boolean. We prove that this is so for finite logics and "projection logics." On the other hand, we show that there exist even concrete non-Boolean logics with a lattice state space (in fact, we prove that every countable concrete logic can be enlarged to a logic with a lattice state space). In the appendix we shortly consider the lattice properties of the set of observables and correct the paper [10].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 81B10, 03G12, 06C15, 46L60

Retrieve articles in all journals with MSC: 81B10, 03G12, 06C15, 46L60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0894439-1
PII: S 0002-9939(1987)0894439-1
Article copyright: © Copyright 1987 American Mathematical Society