Descriptive complexity of the sizes of subsets of groups

• Date: 2017
• Main Authors: Banakh, T. O., Protasov, I. V., Protasova, K. D., Банах, Т. О., Протасов, І. В., Протасова, К. Д.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1780
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the Borel complexity of some basic families of subsets of a countable group (large, small, thin, rarefied, etc.) determined by the sizes of their elements. The obtained results are applied to the Czech – Stone compactification $\beta G$ of the group $G$. In particular, it is shown that the...