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Quantum logics and Lindenbaum property

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Abstract

This paper will take into account the Lindenbaum property in Orthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibility of extending any semantically non-contradictory set of formulas to a semantically non-contradictory complete set of formulas. The main purpose of this paper is to show that both OQL and PCL cannot satisfy the Lindenbaum property.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 5000, Köln 41, West Germany

    Roberto Giuntini

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  1. Roberto Giuntini
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I would like to thank Dr. P. L. Minari and Dr. G. Corsi for many enlightening and encouraging conversations. I am especially grateful to Prof. M. L. Dalla Chiara who sparked my interest in Quantum Logic and Philosophy of Physics.

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Giuntini, R. Quantum logics and Lindenbaum property. Stud Logica 46, 17–35 (1987). https://doi.org/10.1007/BF00396903

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