Title: The descriptive look at the size of subsets of groups,
Abstract: We explore the Borel complexity of some basic families of subsets of a
countable group (large, small, thin, sparse and other) defined by the size of
their elements. Applying the obtained results to the Stone-Čech
compactification $\beta G$ of $G$, we prove, in particular, that the closure of
the minimal ideal of $\beta G$ is of type $F_{\sigma\delta}$.