Algebraic Theory of QuasivarietiesSpringer Science & Business Media, 30.09.1998 - 300 Seiten 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. |
Inhalt
Basic Notions | 1 |
Finitely Presented Structures | 57 |
Subdirectly Irreducible Structures | 103 |
Join Semidistributive Lattices | 141 |
QuasiIdentities on Structures | 245 |
| 295 | |
Häufige Begriffe und Wortgruppen
A₁ Algebra Logic Algebra Universalis algebraic lattice algebraic subset arbitrary assume atomic formulas axiomatizable axiomatizable class B₁ basis of quasi-identities Birkhoff Boolean c₁ cardinality color-family compact element complete lattice congruence Consequently consider convex geometry Corollary decomposition defined definition denote direct products distributive lattice dually Dziobiak easy embedding equivalent exists a homomorphism finite lattice finite number finite signature finitely based finitely presented following assertion free lattice Gorbunov graph H groups homomorphic image homomorphism ƒ identities implies infinite isomorphism join semidistributive lattice K-congruence K₁ l-projective L-structures lattice Lq lattices of quasivarieties Lemma locally finite quasivariety lower-bounded lattice Lq(K Mal'tsev mapping Math modular lattices moreover nonempty nontrivial obvious partially ordered set prevariety PROOF Proposition prove Q-lattices quasivariety relation symbol retract satisfies semigroups semilattice subclass subdirect product subdirectly irreducible sublattice subquasivariety substructure Theorem theory ultraproducts universal Horn class variety