Existence of finite bases for quasi-equations of unary algebras with 0
David Casperson, J. Hyndman, J. Mason, James B. Nation, B. Schaan · International Journal of Algebra and Computation · 2015
A finite unary algebra of finite type with a constant function 0 that is a one-element subalgebra, and whose operations have range {0, 1}, is called a {0, 1}-valued unary algebra with 0. Such an algebra has a finite basis for its quasi-equations if and only if the relation defined by the rows of the nontrivial functions in the clone form an order ideal.