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Undecidable theories of Lyndon algebras

Published online by Cambridge University Press:  12 March 2014

Vera Stebletsova  and
Yde Venema
Vera Stebletsova
Affiliation:
Department of Artificial Intelligence, Faculty of Science, Vrije Universiteit Amsterdam, de Boelelaan 1081A, 1081 HV Amsterdam, The Netherlands, E-mail: Vera.Stebletsova@phil.uu.nl
Yde Venema
Affiliation:
Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, NL-1018 TV Amsterdam, The Netherlands, E-mail: yde@wins.uva.nl
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Abstract

With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 207 - 224
Copyright
Copyright © Association for Symbolic Logic 2001

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