Journal of Symbolic Logic

Undecidable Theories of Lyndon Algebras

Vera Stebletsova and Yde Venema

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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.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 1 (2001), 207-224.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746367

Mathematical Reviews number (MathSciNet)
MR1825181

Zentralblatt MATH identifier
0980.03065

JSTOR
links.jstor.org

Citation

Stebletsova, Vera; Venema, Yde. Undecidable Theories of Lyndon Algebras. J. Symbolic Logic 66 (2001), no. 1, 207--224. https://projecteuclid.org/euclid.jsl/1183746367


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