Let $X$ be a set and $\kappa\leq\lvert X\rvert$ be a cardinal. A $\kappa$-sized subset of $X$ is a subset of $X$ whose cardinality is $\kappa$.
The set of all $\kappa$-sized subsets of $X$ is denoted by
\[\powerset_\kappa(X) = \{A\subseteq X:\lvert A\rvert=\kappa\}.\]