A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let [capital script]M [infinity symbol] [over][subscript italic]n denote the lattice variety generated by all modular lattices of width not exc…
The existence of lattices with trivial automorphism group was shown by O'Meara, who gave an algorithm to construct such a lattice starting from any given lattice. In this process, the discriminants of the lattices increase in each step. Biermann proved the existence of a lattice…
In part I we address the question: which varieties have a decidable first order theory? We confine our attention to varieties whose algebras have modular congruence lattices (i.e., modular varieties), and focus primarily on locally finite varieties, although near the end of the …