Algebraic Theory of Quasivarieties [Hardcover]

The theory of quasivarieties constitutes an independent direction in algebra and mathematical logic and specializes in a fragment of first-order logic-the so-called universal Horn logic. This treatise uniformly presents the principal directions of the theory from an effective algebraic approach developed by the author himself. A revolutionary exposition, this influential text contains a number of results never before published in book form, featuring in-depth commentary for applications of quasivarieties to graphs, convex geometries, and formal languages. Key features include coverage of the Birkhoff-Mal'tsev problem on the structure of lattices of quasivarieties, helpful exercises, and an extensive list of references.Basic Notions. Finitely Presented Structures. Subdirectly Irreducible Structures. Join Semidistributive Lattices. Lattices of Quasivarieties. Quasi-Identities on Structures. Index.