Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
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 Köhler
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.