Computable Folner sequences of amenable groups

The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of groups where finite generation is not assumed. We also initiate some new directions in this topic, for example complexity of families of effective Folner sequences. Possible extensions of this approach to metric groups are also discussed. This paper also contains some unpublished results from the paper of the first author arXiv:1904.02640.