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Undecidable Theories of Lyndon Algebras

Vera Stebletsova and Yde Venema
The Journal of Symbolic Logic
Vol. 66, No. 1 (Mar., 2001), pp. 207-224
DOI: 10.2307/2694918
Stable URL: http://www.jstor.org/stable/2694918
Page Count: 18
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Undecidable Theories of Lyndon Algebras
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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.

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