%0 Journal Article %T Nice enumerations and extreme amenability %A Aleksander Ivanov %J Mathematics %D 2013 %I arXiv %X We study properties related to nice enumerability of countably categorical structures and properties related to extreme amenability of automorphism groups of these structures. The text substantially differs from the previous version. In particular the example of Section 3 is transported to arXiv: 1403.7610. This version is not final. %U http://arxiv.org/abs/1310.7116v2