Non-collapse of the effective Wadge hierarchy

We study the recently suggested effective Wadge hierarchy in spaces, concentrating on non-collapse property. Along with hierarchies of sets, we k-partitions which are interesting their own. In particular, establish sufficient conditions for and apply them to some concrete including discrete space natural numbers, Baire space, Cantor space. While latter two cases obtained by easy effectivization corresponding topological result T. Kihara A. Montalban, first case needs a different technique is certainly main technical this paper.