Quantum logics and Lindenbaum property

Maciej Mączyński

Christian Schindler

E. Giuntini

This paper will take into account the Lindenbaum property in Ortho modular 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 possibi? lity of extending any semantically non-contradictory set of formulas to a semanti? cally non-contradictory complete set of formulas. The main purpose of this paper is4 to show that both OQL and PCL cannot satisfy the Lindenbaum property.

Thomas A. Brody

David Finkelstein

Roberto Giuntini

Abstract The relative Lindenbaum property is considered in orthomodular quantum logic and in partial class ical logic. The properties of these models are connected with the possibility of hidden‐variable reconstruction of particular (1/2‐spin particle e.g.) quantum physical systems.