A Gödel algebra is a Heyting algebra A = (A,∨,0,∧,1,→) such that (x → y)∨(y → x) = 1.
Remark: Gödel algebras are also called linear Heyting algebras since subdirectly irreducible Gödel algebras are linearly ordered Heyting algebras.
A Gödel algebra is a [representable FLew-algebra]? A = (A,∨,0,∧,1,·,→) such that
x∧y = x·y.
Let A and B be Gödel algebras. A morphism from A to B is a function h : A→B that is a homomorphism: h(x∨y) = h(x)∨h(y) and h(0) = 0 and h(x∧y) = h(x)∧h(y) and h(1) = 1 and h(x→y) = h(x)→h(y).
|Congruence n-permutable||yes, n = 2|
|Congruence e-regular||yes, e = 1|
|Congruence extension property||yes|
|Definable principal congruences||yes|
|Equationally definable principal congruences||yes|
|Strong amalgamation property|
|Epimorphisms are surjective|