Varieties of orthomodular lattices related to states
This is a very good paper which should be recommended to anyone interested in orthomodular structures. The main question asked and analyzed there is as follows: Given a preassigned property P of the state space, when the class of all orthomodular lattices whose state spaces satisfy P forms a variety? Apart from the obvious algebraic interest, this question is also relevant to the axiomatics of quantum theories. Using Birkhoff's characterization of varieties, the author develops a method for pursuing the above question. The results which he obtains may in the reviewer's view iniciate a new branch of lattice theory. (As a by- product the paper solves an open question posed by \textit{R. Godowski} [Demonstr. Math. 15, 817-822 (1982; Zbl 0522.06010)].)
scientific article; zbMATH DE number 3929072
scientific article