Definition:Arithmetic Ordered Set

Definition

Let $L = \struct {S, \vee, \preceq}$ be a bounded below join semilattice.

$L$ is arithmetic if and only if

$L$ is algebraic

$\map K L$ is meet closed

where $\map K L$ denotes the compact subset of $L$.

Sources

• Mizar article WAYBEL_8:def 5