We will call a binary relation ú a on the 2w by the redusibility of sets if it is reflexive and transitive. If A ú aB« A ú eB for any sets A and B then ú a is called enumeration reducibility and if A ú aB« A ú T B then ú a is called decision reducibility. We will say that ú a is stronger than ú b if A ú aB« A ú bB for any sets A and B. It is clear that there are such different reducibilities at least 22w. Naturally we consider such reducibilities which have a intuitive base communicated with the effective computability. Some reducibilities are enumerable and decidable simmultaneously. For example the reducibilities of the truth-table type ú m, ú c, ú q, ú p, and also corresponding bounded redusibilities ú bc, ú bq, ú bp are the same.
In the article [1] is constructed the digraph of enumeration reducibilities in which an oriented edge joins more and less strong reducibilies. In addition the new reducibilities ú fe, ú be, ú btte are located in this Cooper's digraph.
We note if ú a,..., ú b is a finite sequence of reducibilities from which at least one is a enumeration reducibility then the relation ú a...b on the 2w such that for any A and B
S. D. Zaharov proposed yet two enumeration redusibilities:
In [3] was introduced new enumeration reducibility ú wpmwhich was called as weak partial m-reducibility
Theorem 1. Dfpm is the upper semilattice with the least element 0 = dwpm(W) where W ¦ ãis c.e.
Theorem 2. Dfpm is not elementary equivalent Dpm.
Theorem 3. The reducibility ú wpm is located in Cooper's digraph.
With the help of such "weakening" of pm - reducibility it is possible to attempt to define new reducibilities. More exactly, let ú a be a reducibility, we define