A semilattice with zero is a structure S = (S,·,0) of type (2,0) such that
(S,·) is a semilattice and
0 is a zero for ·: x·0 = 0.
Let S and T be semilattices with zero. A morphism from S to T is a function h : S→T that is a homomorphism: h(x·y) = h(x)·h(y) and h(0) = 0.
|Equational theory||decidable in PTIME|
|Congruence extension property|
|Definable principal congruences|
|Equationally definable principal congruences|
|Strong amalgamation property|
|Epimorphisms are surjective|