Profinite completion and MacNeille completion can coincide on modal algebras

Seminar series

Analytic Topology in Mathematics and Computer Science

Date

Thu, 10 Jan 2008
10:30

Location

Speaker

Jacob Vosmaer

Organisation

Amsterdam

We show that the profinite completion (a universal algebraic

construction) and the MacNeille completion (an order-theoretic

construction) of a modal algebra $A$ coincide, precisely when the congruences of finite index of $A$ correspond to principal order filters. Examples of such modal algebras are the free K4-algebra and the free PDL-algebra on finitely many generators.