PP-2007-34:
Vosmaer, Jacob
(2007)
*MacNeille completion and profinite completion can coincide on finitely generated modal algebras.*
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## 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 |

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