Undecidable theories of Lyndon algebras (Q2732275)

It is known that Lyndon algebras form an interesting connection between projective geometry and algebraic logic. In this paper, the authors prove that if \(\mathcal G\) is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class \(L({\mathcal G})\) of Lyndon algebras associated with projective geometries in \(\mathcal G\) has an undecidable equational theory. In their proof the authors use a connection between projective geometries and diagonal-free cylindric algebras.