2015-05-26: Paul Levy (Birmingham)

Tue, 14 Oct 2025 16:51:42 +0000

Paul Levy (Birmingham)

Final coalgebras from corecursive algebras

Abstract

We give a technique to construct a final coalgebra out of modal logic. An element of the final coalgebra is a set of modal formulas. The technique works for both the finite and the countable powerset functors. Starting with a corecursive algebra, we coinductively obtain a suitable subalgebra. We see - first with an example, and then in the general setting of modal logic on a dual adjunction - that modal theories form a corecursive algebra, so that this construction may be applied.

We generalize the framework to categories other than Set, and look at examples in Poset and in the opposite category of Set.

2015-05-26 16:00:00 UTC
LT1415