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1.

図書
図書
1. Algebraic logic and universal algebra in computer science : conference, Ames, Iowa, USA, June 1-4, 1988, proceedings (: gw ; : us)
C.H. Bergman, R.D. Maddux, D.L. Pigozzi (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1990  xi, 292 p. ; 25 cm
シリーズ名: Lecture notes in computer science ; 425
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2.

図書
図書
2. Relation algebras. 1st ed
Roger D. Maddux
出版情報: Amsterdam ; Tokyo : Elsevier, 2006  xxvi, 731 p. ; 24 cm
シリーズ名: Studies in logic and the foundations of mathematics ; v. 150
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目次情報: 続きを見る
Preface
List of Figures
List of Tables
Calculus of relations / Chapter 1：
De Morgan, Peirce, and Schroder / 1：
Binary relations / 2：
Complement and converse / 3：
Union and intersection / 4：
Relative multiplication and addition / 5：
More operations / 6：
Four distinguished relations / 7：
Axiomatization of the calculus of relations / 8：
Definitions of relation algebras / 9：
Undecidability and inexpressibility / 10：
Incompleteness / 11：
Representability / 12：
Weakened associativity / 13：
Set theory / Chapter 2：
Classes, equality, membership, sets, and proper classes
Language of set theory
An axiomatization of set theory
Axiom of Extensionality
Virtual classes, names, and notational concerns
Axiom of the Empty Set
Axiom of Complementation
Axiom of Intersection
Calculus of classes
Axiom of Unordered Pairs
Axiom of Relative Product
Axiom of Converse
Axiom of the [epsilon]-Relation
Axioms of the calculus of relations / 14：
Kinds of relations / 15：
Coextensivity / 16：
Functional and injective relations / 17：
Functional and injective parts / 18：
Projection functions / 19：
Boolean and relative operations on sets / 20：
Relation Existence Theorem / 21：
Axiom of Singletons / 22：
Class Union Axiom / 23：
Class Existence Theorem / 24：
Lifting relations to sets / 25：
Replacement Axiom / 26：
Set Union Axiom / 27：
Powerset Axiom / 28：
Partial orderings, meets, joins, and lattices / 29：
Axiom of Infinity / 30：
Axiom of Choice / 31：
Axiom of Regularity / 32：
Ordinals and cardinals / 33：
Dedekind-MacNeille completion / 34：
General algebra / Chapter 3：
Algebraic structures
Subalgebras
Congruence relations and quotients
Homomorphisms
Filters and ideals
Products of algebras
Operators S, H, I, P, Up
Assembly Lemma
Clones
Free algebras
Algebras of sets and relations
Proper relation algebras and RRA
Closure of RRA under subalgebras and products
Relational ideals
S and H commute on proper relation algebras
Peircean ideals
Closure of RRA under homomorphisms
Logic with equality / Chapter 4：
Syntax
Semantics
Axiomatization and formalisms
Formalisms of Tarski-Givant
Soundness
Deduction theorem
Implicational fragment
Completeness of (HI), (HII), (HIII')
Completeness of (LI)-(LIII)
Quantifier axioms
Equality axioms
Axioms for a binary relational language
Quotients of interpretations
Consistent and complete theories
Witnesses
Completeness and compactness
Boolean algebras / Chapter 5：
Axioms R[subscript 1]-R[subscript 3]
Partial orderings, completeness, atoms, density
Meets and joins of subsets
Ideals, filters, and ultrafilters
Functions between Boolean algebras
Congruence relations, ideals, filters, and homomorphisms
Complete additivity and multiplicativity
Completeness and atoms
Duals and conjugates
Regular-open BA of a closure operator
Regular-open BA of a topological closure operator
Topological spaces and closure operators
Complex algebra of a binary relation
Complete BA of a partial ordering
Completion of a BA
Perfect extension of a BA
Summary of constructions
Extending Boolean operators
Composing extended Boolean operators
Extending operators within a BA
Preservation theorems for complete extensions
Relation algebras / Chapter 6：
Boolean relation algebras
Group relation algebras
NA, WA, and SA
Special kinds of elements
Axioms R[subscript 7], R[subscript 8]
Axiom R[subscript 5]
Axioms R[subscript 7], R[subscript 8], R[subscript 9]
Axioms R[subscript 5], R[subscript 7], R[subscript 8], R[subscript 9]
Axioms R[subscript 6], R[subscript 7], R[subscript 9]
Axioms R[subscript 6], R[subscript 7], R[subscript 8], R[subscript 9]
Axioms R[subscript 5], R[subscript 6], R[subscript 7], R[subscript 9]
Axioms R[subscript 5], R[subscript 6], R[subscript 7], R[subscript 8], R[subscript 9]
Axiom R[subscript 10] with others
Theorem K and the cycle law
Special elements in NA
Characterizations of NA and RA
Duality for NA
Completions
Perfect extensions
Matrices of elements
Bases
Elementary arithmetic in WA
Properties of bases
n-dimensional relation algebras
Cycles of atoms
Complex algebras of ternary relations
The very nonassociative algebra in NA [similar] WA
McKinsey's algebra in WA [similar] SA
An algebra in SA [similar] RA
Lyndon's nonrepresentable algebras in RA [similar] RRA
Jonsson's algebras from projective geometries
Lyndon's algebras from projective geometries
McKenzie's nonrepresentable algebra
Allen's interval algebra
Cycle structures of complex algebras / 35：
Representation by complex algebras / 36：
Elementary arithmetic in SA / 37：
Associativity in groupoids / 38：
Independence of seven weak associative laws / 39：
Consequences of 4-associativity / 40：
Relativization / 41：
Ideals / 42：
Ideal elements, relativization, and homomorphisms / 43：
Simplicity / 44：
Direct products / 45：
Necessary subalgebras of SAs / 46：
Elementary arithmetic in RA / 47：
Functional elements / 48：
Transitive and equivalence elements / 49：
Forbidden matrices / 50：
Equational basis for RA[subscript n] / 51：
Equational basis for RRA / 52：
Representation theorems / 53：
Cycles in structures / 54：
Classification of simple finite algebras / 55：
Finite integral relation algebras with 0, 1, 2, or 3 atoms / 56：
Finite integral relation algebras with 4 or 5 atoms / 57：
Cycles of the algebras 1[subscript 37]-37[subscript 37] / 58：
Multiplication tables for algebras 1[subscript 37]-37[subscript 37] / 59：
Diversity cycles for the algebras 1[subscript 65]-65[subscript 65] / 60：
Multiplication tables for the algebras 1[subscript 65]-65[subscript 65] / 61：
Diversity cycles of the algebras 1[subscript 83]-83[subscript 83] / 62：
Multiplication tables for algebras 1[subscript 83]-83[subscript 83] / 63：
Failures of (J), (L), (M) among 1[subscript 1]-1[subscript 83] / 64：
Independence of (J), (L), and (M) / 65：
5-dimensional relational basis data for 198 algebras / 66：
Algebras of every dimension / 67：
Flexible atoms / 68：
Finite algebras with many automorphisms / 69：
Splitting atoms / 70：
RRA is not finitely based / 71：
The number of finite integral relation algebras / 72：
Many nonrepresentable relation algebras / 73：
Algebras with few subalgebras / 74：
Non-embeddable relation algebras / 75：
Complex algebras of cycle structures / 76：
Flexible systems of atoms / 77：
Trails of matrices / 78：
Singletons and twins in a simple SA / 79：
Algebras from modular lattices / 80：
Factor algebras / 81：
A characterization of representability / 82：
Complete representability / 83：
RRAs with no complete representations / 84：
Point-density and pair-density / 85：
Simple pair-dense algebras / 86：
Complete representability results / 87：
Algebraic logic / Chapter 7：
Equipollence of L and L[superscript +]
Inequipollence of L[superscript x] and L[superscript +]
Finite-variable formalisms
Algebras of formulas
Free RRAs of formulas
SAs and RAs of formulas
Algebraic semantics
Algebraic satisfaction and substitution
Algebraic soundness
Free SAs and RAs of formulas
Formalizing set theory in L[superscript x]
4329 finite integral relation algebras / Chapter 8：
Cycles of algebras 1[subscript 1316]-1316[subscript 1316]
Cycles of algebras 1[subscript 3013]-3013[subscript 3013]
Failures of (J), (L), (M) among 1[subscript 1316]-1316[subscript 1316] and 1[subscript 3013]-3013[subscript 3013]
5-dimensional basis data for 1[subscript 1316]-1316[subscript 1316] and 1[subscript 3013]-3013[subscript 3013]
Bibliography
Index
Preface
List of Figures
List of Tables
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