BCK-lattices

Abbreviation: BCKlat

Definition

A BCK-lattice is a structure A = (A,∨,∧,→,1) of type (2,2,2,0) such that

(A,∨,→,1) is a BCK-join-semilattice and
(A,∧,→,1) is a BCK-meet-semilattice.

Remark: x ≤ y   ⇔   x→y = 1 is a partial order, with 1 as greatest element, and ∨, ∧ are a join and meet for this order.

[Pawel M. Idziak, Lattice operation in BCK-algebras, Math. Japon. 29 (1984) 839--846 MRreview]

Morphisms

Let A and B be BCK-lattices. 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(x∧y) = h(x)∧h(y) and h(x→y) = h(x)→h(y) and h(1) = 1.

Some results

Examples

Properties

Finite members

Subclasses

Superclasses