Thu, 10 Jan 2008
10:30
10:30
L3
Profinite completion and MacNeille completion can coincide on modal algebras
Jacob Vosmaer
(Amsterdam)
Abstract
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.