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Decidability problem for finite Heyting algebras

Published online by Cambridge University Press:  12 March 2014

Katarzyna Idziak  and
Pawel M. Idziak
Katarzyna Idziak
Affiliation:
Department of Logic, Jagiellonian University, Cracow, Poland
Pawel M. Idziak
Affiliation:
Department of Logic, Jagiellonian University, Cracow, Poland
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Abstract

The aim of this paper is to characterize varieties of Heyting algebras with decidable theory of their finite members. Actually we prove that such varieties are exactly the varieties generated by linearly ordered algebras. It contrasts to the result of Burris [2] saying that in the case of whole varieties, only trivial variety and the variety of Boolean algebras have decidable first order theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 3 , September 1988 , pp. 729 - 735
Copyright
Copyright © Association for Symbolic Logic 1988

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References

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