Logical independence in quantum logic

Foundations of Physics 25 (3):411-422 (1995)
The projection latticesP(ℳ1),P(ℳ2) of two von Neumann subalgebras ℳ1, ℳ2 of the von Neumann algebra ℳ are defined to be logically independent if A ∧ B≠0 for any 0≠AεP(ℳ1), 0≠BP(ℳ2). After motivating this notion in independence, it is shown thatP(ℳ1),P(ℳ2) are logically independent if ℳ1 is a subfactor in a finite factor ℳ andP(ℳ1),P(ℳ2 commute. Also, logical independence is related to the statistical independence conditions called C*-independence W*-independence, and strict locality. Logical independence ofP(ℳ1,P(ℳ2 turns out to be equivalent to the C*-independence of (ℳ1,ℳ2) for mutually commuting ℳ1,ℳ2 and it is shown that if (ℳ1,ℳ2) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(ℳ1,P(ℳ2 are logically independent in the following cases: ℳ is a finite-dimensional full-matrix algebra and ℳ1,ℳ2 are C*-independent; (ℳ1,ℳ2) is a W*-independent pair; ℳ1,ℳ2 have the property of strict locality
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF02059228
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,440
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.

Add more references

Citations of this work BETA
Reichenbach's Common Cause Principle and Quantum Field Theory.Miklós Rédei - 1997 - Foundations of Physics 27 (10):1309-1321.

Add more citations

Similar books and articles
Quantum Logic as a Fragment of Independence-Friendly Logic.Jaakko Hintikka - 2002 - Journal of Philosophical Logic 31 (3):197-209.
Elementary Prepositions, Independence, and Pictures.Rod Bertolet - 1991 - Journal of Philosophical Research 16:53-61.
Discouraging Results for Ultraimaginary Independence Theory.Itay Ben-Yaacov - 2003 - Journal of Symbolic Logic 68 (3):846-850.
Elementary Propositions and Independence.John L. Bell & William Demopoulos - 1996 - Notre Dame Journal of Formal Logic 37 (1):112-124.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
Dependence and Independence.Erich Grädel & Jouko Väänänen - 2013 - Studia Logica 101 (2):399-410.
Remarks on Independence Proofs and Indirect Reference.Günther Eder - 2013 - History and Philosophy of Logic 34 (1):68-78.
When Can Statistical Theories Be Causally Closed?Balazs Gyenis & Miklos Redei - 2004 - Foundations of Physics 34 (9):1285-1303.
Added to PP index

Total downloads
56 ( #95,373 of 2,180,171 )

Recent downloads (6 months)
1 ( #303,870 of 2,180,171 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums