Definition:Finite Join Property

Definition

Let $\struct {B, \vee, \wedge, \neg, \bot, \top}$ be a Boolean algebra.

Let $J \subseteq B$.

Then $J$ has the finite join property if and only if:

$\forall x_1, x_2, \ldots \in J: x_1 \vee x_2 \vee \dots \vee x_n \ne \top$