New applications of the wreath product of forest algebras

Abstract

We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in CTL and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in PDL ; and new examples of languages outside CTL, along with an application to the question of what properties are definable in both CTL and LTL .