PP-2020-04: Diego's theorem for nuclear implicative semilattices

PP-2020-04: Bezhanishvili, Guram and Bezhanishvili, Nick and Carai, Luca and Gabelaia, David and Ghilardi, Silvio and Jibladze, Mamuka (2020) Diego's theorem for nuclear implicative semilattices. [Pre-print]

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We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients of our proof include the coloring technique and construction of universal models from modal logic. For this we develop duality theory for finite nuclear implicative semilattices, generalizing K¨ohler duality. We
prove that our main result remains true for bounded nuclear implicative semilattices, give an alternative proof of Diego’s Theorem, and provide an explicit description of the free cyclic nuclear implicative semilattice.

Item Type: Pre-print
Report Nr: PP-2020-04
Series Name: Prepublication (PP) Series
Year: 2020
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 07 Feb 2020 21:48
Last Modified: 07 Feb 2020 21:51
URI: https://eprints.illc.uva.nl/id/eprint/1730

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