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algebra universalis

, Volume 42, Issue 3, pp 155–164 | Cite as

Quasivarieties of orthomodular lattices determined by conditions on states

  • R. Mayet
  • P. Pták

Abstract.

In this paper we carry on the research initiated in [13] and [14]. We consider classes of orthomodular lattices which satisfy certain state and polynomial conditions. We show that these classes form quasivarieties. We then exhibit basic examples of these quasivarieties (some of these examples originated in the quantum logic theory). We finally show how the quasivarieties in question can be described in terms of implicative equations. (It should be noted that in some cases we have not been able to clarify whether or not a class shown to be a quasivariety is a variety, see Section 2.)

Key words: orthomodular lattice, state, noncompatible pairs, (quasi)variety. 

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Copyright information

© Birkhäuser Verlag Basel, 1999

Authors and Affiliations

  • R. Mayet
    • 1
  • P. Pták
    • 2
  1. 1.Institut Girard Desargues ESA 5028 du CNRS Universit\'{e} Claude Bernard Lyon 1 F-69622 Villeurbanne Cedex France, e-mail: mayet@desargues.univ-lyon1.fr,FR
  2. 2.Czech Technical University - El. eng. Department of Mathematics CZ-166 27 Prague 6 Czech Republic, e-mail: ptak@math.feld.cvut.cz,CZ

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