Diego's Theorem for nuclear implicative semilattices
Logic
2020-01-31 v1
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.
Cite
@article{arxiv.2001.11060,
title = {Diego's Theorem for nuclear implicative semilattices},
author = {Guram Bezhanishvili and Nick Bezhanishvili and Luca Carai and David Gabelaia and Silvio Ghilardi and Mamuka Jibladze},
journal= {arXiv preprint arXiv:2001.11060},
year = {2020}
}
Comments
40 pages, 11 figures