Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory

Cover
......Page 1
Series
......Page 2
Title
......Page 4
Copyright
......Page 5
Preface
......Page 8
Contents
......Page 10
Introduction
......Page 16
Preliminaries
......Page 32
Part I - Universal Algebra
......Page 36
1. Basic Concepts of Universal Algebra
......Page 40
2. Lattices
......Page 50
3. Hull Systems and Closure Operators
......Page 60
4. Homomorphisms, Congruences and Galois Connections
......Page 66
5. Direct and Subdirect Products
......Page 76
6. Varieties, Equational Classes, and Free Algebras
......Page 86
Part II - Function Algebras
......Page 104
1. Basic Concepts, Notations, and First Properties
......Page 106
2. The Galois-Connection Between Function- and Relation-Algebras
......Page 140
3. The Subclasses of $P_2$
......Page 160
4. The Subclasses of $P_k$ Which Contain $P^1_k$
......Page 174
5. The Maximal Classes of $P_k$
......Page 178
6. Rosenberg's Completeness Criterion for $P_k$
......Page 206
7. Further Completeness Criteria
......Page 226
8. Some Properties of the Lattice $L_k$
......Page 234
9. Congruences and Automorphisms on Function Algebras
......Page 248
10. The Relation Degree and the Dimension of Subclasses of $P_k$
......Page 306
11. On Generating Systems and Orders of the Subclasses of $P_k$
......Page 322
12. Subclasses of $P_{k,2}$
......Page 350
13. Classes of Linear Functions
......Page 398
14. Submaximal Classes of $P_3$
......Page 414
15. Finite and Countably Infinite Sublattices of Depth 1 or 2 of $L_3$
......Page 448
16. The Maximal Classes of $\bigcap _{a\in Q}Pol_k\{a\}$ for $Q ubseteq E_k$
......Page 514
17. Maximal Classes of $Pol_k E_l$ for $2\leq l < k$
......Page 530
18. Further Submaximal Classes of $P_k$
......Page 570
19. Maximal Classes and Minimal Clones of $P_k$
......Page 604
20. Partial Function Algebras
......Page 612
References
......Page 654
Glossary
......Page 670
Index
......Page 678