Definition:Finite Join Property

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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 $x_1, x_2, \dots, x_n \in J$:

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