Orthomodular Lattices

Elżbieta Mądra 1  and Adam Grabowski 1
  • 1 Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok Poland

Orthomodular Lattices

The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.

As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].

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