De nability, Canonical Models, Compactness for Finitary Coalgebraic Modal Logic

This paper studies coalgebras from the perspective of the nitary observations that can be made of their behaviours. Based on the terminal sequence, notions of nitary behaviours and nitary predicates are introduced. A category Behω(T ) of coalgebras with morphisms preserving nitary behaviours is de ned. We then investigate de nability and compactness for nitary coalgebraic modal logic, show that the nal object in Behω(T ) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the nitary part of the terminal sequence.