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arXiv · 2001.11060

Diego's Theorem for nuclear implicative semilattices

Guram Bezhanishvili·Nick Bezhanishvili·Luca Carai·David Gabelaia·Silvio Ghilardi·Mamuka Jibladze
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Abstract

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.

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Guram Bezhanishvili, Nick Bezhanishvili, Luca Carai, David Gabelaia, Silvio Ghilardi, Mamuka Jibladze. 2020-01-29. Diego's Theorem for nuclear implicative semilattices. https://arxiv.org/abs/2001.11060

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