Relation algebras by games:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Amsterdam
North Holland/Elsevier
2002
|
| Edition: | 1st ed |
| Series: | Studies in logic and the foundations of mathematics
v. 147 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise Includes bibliographical references (pages 629-654) and indexes |
| Physical Description: | 1 Online-Ressource (xvii, 691 pages) |
| ISBN: | 9780444509321 0444509321 9780080540450 0080540457 1281048542 9781281048547 |
Staff View
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| 490 | 0 | |a Studies in logic and the foundations of mathematics |v v. 147 | |
| 500 | |a 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 games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. | ||
| 500 | |a In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. | ||
| 500 | |a Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise | ||
| 500 | |a Includes bibliographical references (pages 629-654) and indexes | ||
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| 650 | 7 | |a Universele algebra |2 gtt | |
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Record in the Search Index
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| any_adam_object | |
| author | Hirsch, R., (Robin) |
| author_facet | Hirsch, R., (Robin) |
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| author_sort | Hirsch, R., (Robin) |
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| bvnumber | BV042317283 |
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| dewey-full | 511/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.3 |
| dewey-search | 511/.3 |
| dewey-sort | 3511 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| id | DE-604.BV042317283 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444509321 0444509321 9780080540450 0080540457 1281048542 9781281048547 |
| language | English |
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| spelling | Hirsch, R., (Robin) Verfasser aut Relation algebras by games Robin Hirsch, Ian Hodkinson 1st ed Amsterdam North Holland/Elsevier 2002 1 Online-Ressource (xvii, 691 pages) txt rdacontent c rdamedia cr rdacarrier Studies in logic and the foundations of mathematics v. 147 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 games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise Includes bibliographical references (pages 629-654) and indexes Algèbres des relations Jeux, Théorie des MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Game theory fast Relation algebras fast Algebraïsche logica gtt Relaties (logica) gtt Speltheorie gtt Universele algebra gtt Relation algebras Game theory Relationenalgebra (DE-588)4206494-6 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Relationenalgebra (DE-588)4206494-6 s Spieltheorie (DE-588)4056243-8 s 1\p DE-604 Hodkinson, Ian Sonstige oth http://www.sciencedirect.com/science/book/9780444509321 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hirsch, R., (Robin) Relation algebras by games Algèbres des relations Jeux, Théorie des MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Game theory fast Relation algebras fast Algebraïsche logica gtt Relaties (logica) gtt Speltheorie gtt Universele algebra gtt Relation algebras Game theory Relationenalgebra (DE-588)4206494-6 gnd Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4206494-6 (DE-588)4056243-8 |
| title | Relation algebras by games |
| title_auth | Relation algebras by games |
| title_exact_search | Relation algebras by games |
| title_full | Relation algebras by games Robin Hirsch, Ian Hodkinson |
| title_fullStr | Relation algebras by games Robin Hirsch, Ian Hodkinson |
| title_full_unstemmed | Relation algebras by games Robin Hirsch, Ian Hodkinson |
| title_short | Relation algebras by games |
| title_sort | relation algebras by games |
| topic | Algèbres des relations Jeux, Théorie des MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Game theory fast Relation algebras fast Algebraïsche logica gtt Relaties (logica) gtt Speltheorie gtt Universele algebra gtt Relation algebras Game theory Relationenalgebra (DE-588)4206494-6 gnd Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Algèbres des relations Jeux, Théorie des MATHEMATICS / Infinity MATHEMATICS / Logic Game theory Relation algebras Algebraïsche logica Relaties (logica) Speltheorie Universele algebra Relationenalgebra Spieltheorie |
| url | http://www.sciencedirect.com/science/book/9780444509321 |
| work_keys_str_mv | AT hirschrrobin relationalgebrasbygames AT hodkinsonian relationalgebrasbygames |