Ternary discriminator

Summary

The ternary discriminator on a set $A$ is the operation $t(x, y, z)$ that returns $z$ when $x = y$ and returns $x$ otherwise. It tests whether two elements are equal and chooses its output accordingly. Algebras in which this operation is a term operation are called quasi-primal when they are finite. Classes of algebras sharing a term for it generate discriminator varieties, which have a very clear structure theory.