Definition:Finite Join Property

Definition
Let $(B, \vee, \wedge, \neg, \bot, \top)$ be a Boolean algebra.

Let $J \subseteq B$.

Then $J$ has the finite join property iff for any $x_1, x_2, \dots, x_n \in J$:


 * $x_1 \vee x_2 \vee \dots \vee x_n \ne \top$