Displaying similar documents to “Laminations, or How to Build a Quantum-Logic-Valued Model of Set Theory.”

Relatively additive states on quantum logics

Pavel Pták, Hans Weber (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we carry on the investigation of partially additive states on quantum logics (see [2], [5], [7], [8], [11], [12], [15], [18], etc.). We study a variant of weak states — the states which are additive with respect to a given Boolean subalgebra. In the first result we show that there are many quantum logics which do not possess any 2-additive central states (any logic possesses an abundance of 1-additive central state — see [12]). In the second result we construct a finite...

Ring-like structures with unique symmetric difference related to quantum logic

Dietmar Dorninger, Helmut Länger, Maciej Maczyński (2001)

Discussiones Mathematicae - General Algebra and Applications

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Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.

Book Reviews

Anatolij Dvurečenskij (2005)

Mathematica Slovaca

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On joint distribution in quantum logics. I. Compatible observables

Anatolij Dvurečenskij (1987)

Aplikace matematiky

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The notion of a joint distribution in σ -finite measures of observables of a quantum logic defined on some system of σ -independent Boolean sub- σ -algebras of a Boolean σ -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.