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Equations in free topoboolean algebra. (English. Russian original) Zbl 0624.03007
Algebra Logic 25, 109-127 (1986); translation from Algebra Logika 25, No. 2, 172-204 (1986).
Let $$\Lambda$$ be a modal or superintuitionistic logic and $$F_{\omega}(\Lambda)$$ the free algebra of rank $$\omega$$ in the variety of algebras corresponding to $$\Lambda$$. For each of the logics S4 and Int the author obtains the following main results. Let $$\Sigma_ f$$ be the signature of $$F_{\omega}(\Lambda)$$ enriched by the free generators as constant operations. Then: 1) The universal theory of $$F_{\omega}(\Lambda)$$ is decidable and there exists an algorithm constructing an obstacle (i.e., roughly speaking, a counter-example) for those universal formulas of $$\Sigma_ f$$ that are false in $$F_{\omega}(\Lambda)$$. 2) There exists an algorithm verifying the solvability of equations in $$F_{\omega}(\Lambda)$$ and finding the solutions of solvable equations.
Reviewer: S.Rudeanu

##### MSC:
 03B25 Decidability of theories and sets of sentences 03G10 Logical aspects of lattices and related structures 06B25 Free lattices, projective lattices, word problems 08B20 Free algebras
##### Keywords:
modal logic; superintuitionistic logic; free algebra; S4; Int
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##### References:
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