Relation Algebras by Games, Volume 147Gulf Professional Publishing, 15 ago 2002 - 691 pagine 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.
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Sommario
Introduction | 1 |
Algebras of Relations | 23 |
Preliminaries | 25 |
Binary relations and relation algebra | 99 |
Examples of relation algebras | 133 |
Relativisation and cylindric algebras | 151 |
Other approaches to algebras of relations | 199 |
Games | 213 |
Relational cylindric and hyperbases | 363 |
Approximations to RRA | 399 |
Constructing Relation Algebras | 439 |
Strongly representable relation algebra atom structures | 445 |
Nonfinite axiomatisability of SRaCAn+1 over SRaCAn | 463 |
The rainbow construction for relation algebras | 491 |
Applying the rainbow construction | 513 |
Decidability | 537 |
Games and networks | 217 |
Axiomatising representable relation algebras and cylindric algebras | 261 |
Axiomatising pseudoelementary classes | 273 |
Game trees | 309 |
Atomic networks | 335 |
Approximations | 353 |
Undecidability of the representation problem for finite algebras | 539 |
Finite base property | 581 |
Epilogue | 607 |
Brief summary | 609 |
Problems | 625 |
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