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An equational theory for \(\sigma \)-complete orthomodular lattices

  • Hector FreytesEmail author
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Abstract

The condition of \(\sigma \)-completeness related to orthomodular lattices places an important role in the study of quantum probability theory. In the framework of algebras with infinitary operations, an equational theory for the category of \(\sigma \)-complete orthomodular lattices is given. In this structure, we study the congruences theory and directly irreducible algebras establishing an equational completeness theorem. Finally, a Hilbert style calculus related to \(\sigma \)-complete orthomodular lattices is introduced and a completeness theorem is obtained.

Keywords

\(\sigma \)-Complete orthomodular lattices Infinitary operations Hilbert style calculus 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of CagliariCagliariItaly
  2. 2.Department of MathematicsUniversity of CagliariCagliariItaly

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