A Boolean algebra with operators is a structure A = (A,∨,0, ∧,1,¬,fi (i ∈ I)) such that
(A,∨,0,∧,1,¬) is a Boolean algebra,
fi is join-preserving in each argument: fi( . . .,x∨y, . . .) = fi( . . .,x, . . .)∨fi( . . .,y, . . .), and
fi is normal in each argument: fi( . . .,0, . . .) = 0 for each i ∈ I.
Let A and B be Boolean algebras with operators of the same signature. A morphism from A to B is a function h : A→B that is a Boolean homomorphism and preserves all the operators: h(fi(x0, . . .,xn−1)) = fi(h(x0), . . .,h(xn−1)).
|Congruence n-permutable||yes, n = 2|
|Congruence extension property||yes|
|Definable principal congruences||no|
|Equationally definable principal congruences||no|
|Strong amalgamation property||yes|
|Epimorphisms are surjective||yes|