The fundamental theorem of finite semidistributive lattices

We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff’s Distributive Lattices. Our FTFSDL is the form “A poset L finite semidistributive lattice if and only there exists set with some additional structure, such that isomorphic to admissible subsets ordered by inclusion; in this case, its structure are uniquely determined L.” The combinatorial abstraction notion torsion pairs from representation theory has geometric meaning case posets regions hyperplane arrangements. show how clarifies many constructions theory, as canonical join representations passing quotients, property interacts other major classes lattices. Many our results also apply infinite