PP-2007-34: Vosmaer, Jacob (2007) MacNeille completion and profinite completion can coincide on finitely generated modal algebras. [Report]
Preview |
Text (Full Text)
PP-2007-34.text.pdf Download (150kB) | Preview |
![[thumbnail of Abstract]](https://eprints.illc.uva.nl/style/images/fileicons/text.png) |
Text (Abstract)
PP-2007-34.abstract.txt Download (745B) |
Abstract
Following [Bezhanishvili & Vosmaer 2007] we confirm a conjecture of
Yde Venema by piecing together results from various
authors. Specifically, we show that if $\mathbb{A}$ is a residually
finite, finitely generated modal algebra such that
$\operatorname{HSP}(\mathbb{A})$ has equationally definable principal
congruences, then the profinite completion of $\mathbb{A}$ is the
MacNeille completion of $\mathbb{A}$, and $\Diamond$ is
smooth. Specific examples of such modal algebras are the free
$\mathbf{K4}$-algebra and the free $\mathbf{PDL}$-algebra.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2007-34 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2007 |
| Uncontrolled Keywords: | modal algebras; MacNeille completion; profinite completion |
| Date Deposited: | 12 Oct 2016 14:36 |
| Last Modified: | 12 Oct 2016 14:36 |
| URI: | https://eprints.illc.uva.nl/id/eprint/268 |
Actions (login required)
 |
View Item |
