 The notions studied in computability theory have the informal property that "A" is reducible to "B" if and only if any (possibly noneffective) decision procedure for "B" can be effectively converted to a decision procedure for "A".The different reducibility relations vary in the methods they permit such a conversion process to use.Every reducibility relation (in fact, every preorder) induces an equivalence relation on the powerset of the natural numbers in which two sets are equivalent if and only if each one is reducible to the other.