Splitting Theorems and the Jump Operator

We investigate the relationship of (jumps of) the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low2. ∗ Research partially supported by the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell University Contract DAAL03-91-C-0027, the IGC of Victoria University and the Marsden Fund for Basic Science under grant VIC-509. § Research partially supported by NSF Grant DMS-9503503 and the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell University Contract DAAL0391-C-0027. 1 

• Type: Journal
• Year: 1998
• Where: APAL
• Authors: Rodney G. Downey, Richard A. Shore
• Keywords: APAL 1998, Cornell University Contract, Mathematical Sciences, Proper Splittings