Equations in free topoboolean algebra (Q1092029)

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.