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Constructible Models of Orthomodular Quantum Logics.

WILCZEK, Piotr (2008) Constructible Models of Orthomodular Quantum Logics. [Preprint]

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Abstract

We continue in this article the abstract algebraic treatment of quantum sentential logics <cite>Wil</cite>. The Notions borrowed from the field of Model Theory and Abstract Algebraic Logic - AAL (i.e., consequence relation, variety, logical matrix, deductive filter, reduced product, ultraproduct, ultrapower, Frege relation, Leibniz congruence, Suszko congruence, Leibniz operator) are applied to quantum logics. We also proved several equivalences between state property systems (Jauch-Piron-Aerts line of investigations) and AAL treatment of quantum logics (corollary 18 and 19). We show that there exist the uniquely defined correspondence between state property system and consequence relation defined on quantum logics. We also signalize that a metalogical property - Lindenbaum property does not hold for the set of quantum logics.


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Item Type: Preprint
Creators:
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WILCZEK, Piotr
Additional Information: This article will appear in International Journal of Theoretic Physics
Keywords: abstract algebraic logic (AAL); model theory; consequence relation; logical matrix; Sasaki deductive filter; state of experimental provability; state property system; orthogonality relation; Lindenbaum property
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Piotr WILCZEK
Date Deposited: 23 May 2008
Last Modified: 07 Oct 2010 15:16
Item ID: 4032
URI: http://philsci-archive.pitt.edu/id/eprint/4032

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