Fixed points of modal schemes (Q1317626)

The concepts of a \(\Sigma\)-formula and \(\Sigma\)-scheme are used in pedicate calculus [\textit{S. S. Goncharov} and \textit{D. I. Sviridenko}, Vychisl. Sist. 107, 3-29 (1985; Zbl 0628.03015)]. In this paper we transfer them to modal propositional logic, which holds a position between classical propositional and predicate logics. In our case, the use of schemes considerably, but not completely, simplifies the situation as compared to that in the predicate logic setting. We prove that a scheme over a transitive Kripke model arrives at its least fixed point in finitely many steps, and that this point is definable by suitable formulas.