Contenuti:
Preliminaries.- I Lattices.- §1. Definitions of Lattices.- §2. Isomorphic Lattices, and Sublattices.- §3. Distributive and Modular Lattices.- §4. Complete Lattices, Equivalence Relations, and Algebraic Lattices.- §5. Closure Operators.- II The Elements of Universal Algebra.- §1. Definition and Examples of Algebras.- §2. Isomorphic Algebras, and Subalgebras.- §3. Algebraic Lattices and Subuniverses.- §4. The Irredundant Basis Theorem.- §5. Congruences and Quotient Algebras.- §6. Homomorphisms and the Homomorphism and Isomorphism Theorems.- §7. Direct Products, Factor Congruences, and Directly Indecomposable Algebras.- §8. Subdirect Products, Subdirectly Irreducible Algebras, and Simple Algebras.- §9. Class Operators and Varieties.- §10. Terms, Term Algebras, and Free Algebras.- §11. Identities, Free Algebras, and Birkhoff’s Theorem.- §12. Mal’cev Conditions.- §13. The Center of an Algebra.- §14. Equational Logic and Fully Invariant Congruences.- III Selected Topics.- §1. Steiner Triple Systems, Squags, and Sloops.- §2. Quasigroups, Loops, and Latin Squares.- §3. Orthogonal Latin Squares.- §4. Finite State Acceptors.- IV Starting from Boolean Algebras.- § 1. Boolean Algebras.- §2. Boolean Rings.- §3. Filters and Ideals.- §4. Stone Duality.- §5. Boolean Powers.- §6. Ultraproducts and Congruence-distributive Varieties.- §7. Primal Algebras.- §8. Boolean Products.- §9. Discriminator Varieties.- §10. Quasiprimal Algebras.- §11. Functionally Complete Algebras and Skew-free Algebras.- §12. Semisimple Varieties.- §13. Directly Representable Varieties.- V Connections with Model Theory.- §1. First-order Languages, First-order Structures, and Satisfaction.- §2. Reduced Products and Ultraproducts.- §3. Principal Congruence Formulas.- §4. Three Finite Basis Theorems.- §5. Semantic Embeddings and Undecidability.- Recent Developments and Open Problems.- Author Index.
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