On models for propositional dynamic logic (Q1183594)

Solving a problem posed by \textit{R. Parikh} [Lect. Notes Comp. Sci. 125, 102-144 (1981; Zbl 0468.68038)], the authors prove for propositional dynamic logic the existence of a universal Kripke model, whose characteristic algebra is initial in the class of *-continuous dynamic algebras. Using it they get easy proofs for the completeness of the Segerberg approximation and the small model theorem of \textit{M. J. Fischer} and \textit{R. E. Ladner} [J. Comput. Syst. Sci. 18, 194-211 (1979; Zbl 0408.03014)]. Finally they give a complete,but infinitary axiomatization which includes a kind of \(\omega\)-rule.