Lattice embeddings below a nonlow2 recursively enumerable degree

We introduce techniques that allow us to embed below an arbitary nonlow₂ recursively enumerable degree any lattice currently known to be embeddable into the recursively enumerable degrees. Research partially supported by NSF Grants DMS-9204308, DMS-93-44740, a US-NZ binational grant NSF 90-20558, the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell Univrsity Contract DAAL03-91-C-0027 and the IGC of Victoria University.