Decision problem for orthomodular lattices |
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Authors: | MAEH Sherif |
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Institution: | (1) Institute of Mathematics Gdańsk University,Wita Stwosza 57, PL- 80-952 Gdańsk-Oliwa, Poland. E-mail: , |
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Abstract: | This paper answers a question of H. P. Sankappanavar who asked whether the theory of orthomodular lattices is recursively
(finitely) inseparable (question 9 in 10]). A very similar question was raised by Stanley Burris at the Oberwolfach meeting
on Universal Algebra, July 15–21, 1979, and was later included in G. Kalmbach’s monograph 6] as the problem 42. Actually
Burris asked which varieties of orthomodular lattices are finitely decidable. Although we are not able to give a full answer
to Burris’ question we have a contribution to the problem. Note here that each finitely generated variety of orthomodular
lattices is semisimple arithmetical and therefore directly representable. Consequently each such a variety is finitely decidable.
(For a generalization of this, i.e. a characterization of finitely generated congruence modular varieties that are finitely
decidable see 5].) In section 3, we give an example of finitely decidable variety of orthomodular lattices that is not finitely
generated.
Received June 28, 1995; accepted in final form June 27, 1996. |
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