an:04012567
Zbl 0624.03007
Rybakov, V. V.
Equations in free topoboolean algebra
EN
Algebra Logic 25, 109-127 (1986); translation from Algebra Logika 25, No. 2, 172-204 (1986).
00152452
1986
j
03B25 03G10 06B25 08B20
modal logic; superintuitionistic logic; free algebra; S4; Int
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.
S.Rudeanu