MacNeille completion and profinite completion can coincide on finitely generated modal algebras |
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Authors: | Jacob Vosmaer |
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Affiliation: | 1. Postbus 94242, 1090 GE, Amsterdam, The Netherlands
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Abstract: | Following Bezhanishvili and Vosmaer, 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 HSP( ${mathbb{A}}$ ) has equationally definable principal congruences, then the profinite completion of ${mathbb{A}}$ is isomorphic to its MacNeille completion, and ? is smooth. Specific examples of such modal algebras are the free K4-algebra and the free PDL-algebra. |
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