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221028  eng 
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a 0080540457

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a 9780080540450

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a 0444509321

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a 9780444509321

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a 1281048542

050 

4 
a QA10

100 
1 

a Hirsch, R.

245 
0 
0 
a Relation algebras by games
c Robin Hirsch, Ian Hodkinson

250 


a 1st ed

260 


a Amsterdam
b North Holland/Elsevier
c 2002, 2002

300 


a xvii, 691 pages
b illustrations

505 
0 

a Introduction  Preliminaries  Binary relations and relation algebra  Examples of relation algebras  Relativisation and cylindric algebras  Other approaches to algebras of relations  Games and networks  Axiomatising representable relation algebras and cylindric algebras  Axiomatising pseudoelementary classes  Game trees  Atomic networks  Relational, cylindric, and hyperbases  Approximations to RRA  Strongly representable relation algabra atom structures  Nonfinite axiomatisability of SRaCAn+1 over SRaCAn  The rainbow construction for relation algebras  Applying the rainbow construction  Undecidability of the representation problem for finite algebras  Finite base property  Brief summary  Problems

505 
0 

a Includes bibliographical references (pages 629654) and indexes

653 


a Algèbres des relations

653 


a Game theory / http://id.loc.gov/authorities/subjects/sh85052941

653 


a Game Theory

653 


a Relationenalgebra / gnd / http://dnb.info/gnd/42064946

653 


a Game theory / fast / (OCoLC)fst00937501

653 


a MATHEMATICS / Logic / bisacsh

653 


a Speltheorie / gtt

653 


a Spieltheorie / gnd / http://dnb.info/gnd/40562438

653 


a Algebraisierbare Logik / gnd / http://dnb.info/gnd/42100732

653 


a Relation algebras / http://id.loc.gov/authorities/subjects/sh93006695

653 


a Relaties (logica) / gtt

653 


a Relation algebras / fast / (OCoLC)fst01093574

653 


a Universele algebra / gtt

653 


a Algebraïsche logica / gtt

653 


a MATHEMATICS / Infinity / bisacsh

653 


a Modelltheorie / gnd / http://dnb.info/gnd/41146177

653 


a Théorie des jeux

700 
1 

a Hodkinson, Ian

041 
0 
7 
a eng
2 ISO 6392

989 


b ZDB1ELC
a Elsevier eBook collection Mathematics

490 
0 

a Studies in logic and the foundations of mathematics

776 


z 9780080540450

776 


z 0080540457

856 
4 
0 
u https://www.sciencedirect.com/science/bookseries/0049237X/147
x Verlag
3 Volltext

082 
0 

a 511/.3

520 


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.

520 


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 nonfinitely axiomatisable or even nonelementary. 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 selfcontained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of firstorder logic and set theory is assumed, though many of the definitions are given.

520 


a Chapter 2 introduces the necessary universal algebra and model theory, and more specific modeltheoretic ideas are explained as they arise
