UID:
almahu_9947367719202882
Format:
1 online resource (711 p.)
Edition:
1st ed.
ISBN:
1-281-04854-2
,
9786611048549
,
0-08-054045-7
Series Statement:
Studies in logic and the foundations of mathematics, v. 147
Content:
Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and g
Note:
Description based upon print version of record.
,
Cover; Contents; Preface; Foreword; Chapter 1. Introduction; 1.1 History; 1.2 To the games; 1.3 Non-finite axiomatisability; 1.4 Approximations to representability; 1.5 Constructions of algebras; 1.6 Some remarks on methods; 1.7 Summary of contents; Part I: Algebras of Relations; Chapter 2. Preliminaries; 2.1 Foundations; 2.2 Model theory; 2.3 Boolean algebras; 2.4 Products and ultraproducts; 2.5 Boolean algebras with operators; 2.6 Varieties and quasi-varieties of BAOs; 2.7 Aspects of duality for BAOs; Chapter 3. Binary relations and relation algebra; 3.1 Algebraic logic
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3.2 Binary relations3.3 Relation algebras; 3.4 Representations of relation algebras; Chapter 4. Examples of relation algebras; 4.1 Set algebras; 4.2 Group relation algebras; 4.3 n-variable logic; 4.4 Examples; 4.5 The Lyndon algebras; Chapter 5. Relativisation and cylindric algebras; 5.1 Relativisation; 5.2 Weakly representable relation algebras; 5.3 Cylindric algebras; 5.4 Substitutions in cylindric algebras; 5.5 Relativised cylindric algebras; 5.6 Relation algebra reducts of cylindric algebras; 5.7 Relation algebra reducts of other cylindric-type algebras
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Chapter 6. Other approaches to algebras of relations6.1 Diagonal-free algebras; 6.2 Polyadic algebra; 6.3 Pinter's substitution algebras; 6.4 Finitisation problem; 6.5 Decidability; 6.6 Amalgamation; 6.7 Technical innovations; 6.8 Applications; Part II: Games; Chapter 7. Games and networks; 7.1 Networks; 7.2 Refining networks; 7.3 All weakly associative algebras have relativised representations; 7.4 Games on relation algebra networks; 7.5 Strategies; 7.6 Games and representations of relation algebras; 7.7 Networks for cylindric algebras; 7.8 Games for cylindric algebra networks
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7.9 Games for temporal constraint handling7.10 Summary of chapter; Chapter 8. Axiomatising representable relation algebras and cylindric algebras; 8.1 The relation algebra case; 8.2 An axiomatisation using 'Q-operators'; 8.3 Axiomatising RCAd for 3 〈= d 〈 ?; 8.4 Axiomatising RCA a for infinite a; Chapter 9. Axiomatising pseudo-elementary classes; 9.1 Introduction; 9.2 Pseudo-elementary classes; 9.3 Examples; 9.4 Model theory of pseudo-elementary classes; 9.5 More explicit axioms; 9.6 Axiomatising pseudo-elementary classes; 9.7 Generalised Q-operators; Chapter 10. Game trees
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10.1 Trees, and games on them10.2 Strategies; 10.3 Examples; 10.4 Formulas expressing a winning strategy; 10.5 Games and non-finite axiomatisability; Chapter 11. Atomic networks; 11.1 Introduction; 11.2 Atomic networks and games; 11.3 Alternative views of the game; 11.4 Atomic games and complete representations; 11.5 Axioms for complete representability?; Part III: Approximations; Chapter 12. Relational, cylindric, and hyperbases; 12.1 Hypernetworks; 12.2 Relational bases and hyperbases; 12.3 Elementary properties of bases; 12.4 Games; 12.5 The variety RAn; 12.6 Maddux's bases
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12.7 Cylindric bases and homogeneous representations
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English
Additional Edition:
ISBN 0-444-50932-1
Language:
English
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