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Decision Problems for Equational Theories of Relation Algebras

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Brand new. We distribute directly for the publisher. This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation ... algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jnsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given.The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic. Read more Show Less

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Overview

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.

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For graduate students, research mathematicians, and computer scientists interested in computability in algebra, logic, and computer science, offers a systematic study of decision problems for equational theories of algebras of binary relations. Develops methods that show promise of wide application, and investigates the complexity of intervals of the theories with respect to questions of decidability. Drawing on ideas going back to J<'o>nsson and Lyndon, shows that such intervals can have the same complexity as the lattice of the subsets of the set of natural numbers. Annotation c. by Book News, Inc., Portland, Or.
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