Decision Problems for Equational Theories of Relation Algebras

Decision Problems for Equational Theories of Relation Algebras

by Hajnal Andreka, Steven R. Givant, Istvan Nemeti
     
 

ISBN-10: 0821805959

ISBN-13: 9780821805954

Pub. Date: 04/14/1997

Publisher: American Mathematical Society

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

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.

Product Details

ISBN-13:
9780821805954
Publisher:
American Mathematical Society
Publication date:
04/14/1997
Series:
Memoirs of the American Mathematical Society Series, #126
Pages:
126

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