Undecidable theories of Lyndon algebras
Yde Venema, Vera Stebletsova
Abstract:
With each projective geometry we can associate a Lyndon algebra.
This 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 $\sG$ has an undecidable
equational theory. In our proof we develop and use a connection
between projective geometries and diagonal-free cylindric algebras.