Boolean algebras with operators

Abbreviation: BAO

Definition

A Boolean algebra with operators is a structure A = (A,∨,0, ∧,1,¬,f_i (i ∈ I)) such that

(A,∨,0,∧,1,¬) is a Boolean algebra,
f_i is join-preserving in each argument:   f_i( . . .,x∨y, . . .) = f_i( . . .,x, . . .)∨f_i( . . .,y, . . .), and
f_i is normal in each argument:   f_i( . . .,0, . . .) = 0 for each i ∈ I.

Morphisms

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(f_i(x₀, . . .,x_n−1)) = f_i(h(x₀), . . .,h(x_n−1)).

Some results

Examples

Properties

Subclasses

Superclasses