Abstract
In this paper we study some foundational aspects of the theory of PDL. We prove a claim made by Parikh (1981), namely, the existence of a Kripke model U that is universal in the sense that every other Kripke model M can be isomorphically embedded in it. Using this model we give different and particularly easy proofs of the completeness theorem for the Segerberg axiomatization of PDL and the small model theorem. We also give an infinitary axiomatization for PDL and prove it to be complete using a syntax model A , by a technique that is well-known from modal logic. We prove that U and A are isomorphic. Finally, we briefly turn to dynamic algebras and show that the characteristic algebra of ??? is initial in the class of ∗-continuous dynamic algebras.
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