Definition:Join Semilattice/Definition 2

Definition

Let $\struct {S, \vee}$ be a semilattice.

Let $\preceq$ be the ordering on $S$ defined by:

$a \preceq b \iff \paren {a \vee b} = b$

Then the ordered structure $\struct {S, \vee, \preceq}$ is called a join semilattice.