In this paper we extend the approach of M. Cavaleri to effective amenability class computably enumerable groups, i.e. in particular do not assume that groups are finitely generated. case computable also study complexity set all F{\o}lner sequences and paradoxical decomposition. appendix attach a version "On decidability groups" by K. Duda A. Ivanov which covers Sections 9 10 from previous versi...

We show normalisation and decidability of convertibility for a type theory with hierarchy universes proof irrelevant propositions, close to the system used in assistant Lean. Contrary previous arguments, does not require explicitly introduce notion neutral normal forms.