The boolean hierarchy of NP-partitions

We introduce the boolean hierarchy of k-partitions over NP for k≥3 as a generalization of the boolean hierarchy of sets (i.e., 2-partitions) over NP. Whereas the structure of the latter hierarchy is rather simple the structure of the boolean hierarchy of k-partitions over NP for k≥3 turns out to be much more complicated. We formulate the Embedding Conjecture which enables us to get a complete idea of this structure. This conjecture is supported by several partial results.