Abstract
We relate three different, but equivalent, ways to characterise behavioural equivalence for set coalgebras. These are: using final coalgebras, using coalgebraic languages that have the Hennessy- Milner property and using coalgebraic languages that have “logical congruences”. On the technical side the main result of our paper is a straightforward construction of the final T-coalgebra of a set functor using a given logical language that has the Hennessy-Milner property with respect to the class of T-coalgebras.
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