Representations of bounded distributive lattices as the continuous sections of Sheaves based on the Priestly and Zarski topologies
Tarek Sayed Ahmed · arXiv (Cornell University) · 2013
Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem of of distributive bounded lattices expanded by modalities (functions distributing over joins) as the continuous sections of sheaves. Our representation is defined via a contravariant functor. We give applications to many-valued logics logics and various modifications of first order logic and multi-modal logic, set in an algebraic framework.