Miroslav Haviar – Dualities for prioritised default bilattices II

Matej Bel University, Slovakia
In the companion talk preceding this one, a new family of prioritised default bilattices, $J_n$, for $n \in \omega$, was introduced. A natural duality for the variety $V_n$ generated by $J_n$ was presented. The objects of the dual category $X_n$ are multi-sorted topological structures. In this talk we give a description and an axiomatisation of the dual category $X_n$. We moreover claim that the category $X_n$ is isomorphic to a category $Y_n$ of single-sorted topological structures. The objects of $Y_n$ are Priestley spaces endowed with a continuous retraction in which the order has a natural ranking. As a nice application we show that the size of the free algebra $F_{V_n}(1)$ is given by a polynomial in $n$ of degree six.

This is joint work with Brian A. Davey and Andrew P.K. Craig