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Decidability Problem for Finite Heyting Algebras

Katarzyna Idziak and Pawel M. Idziak
The Journal of Symbolic Logic
Vol. 53, No. 3 (Sep., 1988), pp. 729-735
DOI: 10.2307/2274568
Stable URL: http://www.jstor.org/stable/2274568
Page Count: 7
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Decidability Problem for Finite Heyting Algebras
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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.

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