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