Optimal strong Mal'cev conditions for omitting type 1 in locally finite varieties

Abstract

We show that the class of locally finite varieties omitting type 1 has the following properties. This class is:(1)definable by an idempotent, linear, strong Mal'cev condition in a language with one 4-ary function symbol; (2) not definable by an idempotent, linear, strong Mal'cev condition in a language with only one function symbol of arity strictly less than 4; (3) definable by an idempotent, linear, strong Mal'cev condition in a language with two 3-ary function symbols; (4) not definable by an idempotent, linear, strong Mal'cev condition in a language with function symbols of arity less than 4 unless at least two of the symbols have arity 3. © 2014 Springer Basel.