Given a set AAA, its finite powerset Pfin(A)\mathcal{P}_\text{fin}(A)Pfin(A) is defined to be the set of its finite powersets.
In symbols:
Pfin(A)={X⊆A∣A finite} \mathcal{P}_\text{fin}(A) = \{ X \subseteq A \mid A \text{ finite} \} Pfin(A)={X⊆A∣A finite}