Definability in Dynamic Logic

Abstract

We study the expressive power of various versions of Dynamic Logic and compare them with each other as well as with standard languages in the logical literature. One version of Dynamic Logic is equivalent to the infinitary logic LCKω1,ω,, but regular Dynamic Logic is strictly less expressive. In particular, the ordinals ωω and ωω.2 are indistinguishable by formulas of regular Dynamic Logic.