Karol Borsuk 1905–1982

Abstract

In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. The main results of the paper concern some new directions in this approach. In the case of computable groups we study decidability of amenability of finitely generated subgroups, complexity of the set of all effective Følner sequences and effective paradoxical decomposition.