Quantum logics and Lindenbaum property

✍ Scribed by Roberto Giuntini

• Publisher: Springer Netherlands
• Year: 1987
• Tongue: English
• Weight: 995 KB
• Volume: 46
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00396903

✦ Synopsis

This paper will t~ke into account the Lindenbaum property in 0rthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). Tho Lindenbaum property has an interes~ both from a logical and a physical poin~ of view since i~ 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. * 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. IV[. L. Dalla Chiara who sparked my interest in Quantum Logic and Philosophy of Physics. 1 An alternative characterization of OQL can be carried out by means of Kripke--style seman%ies [8], [4].