The Journal of Symbolic Logic

Research Article

Degrees joining to 0

David B. Posnera1 and Robert W. Robinsona2

a1 San Jose State University, San Jose, California 95192

a2 University of Newcastle, New South Wales, Australia 2308


It is shown that if and are sets of degrees uniformly recursive in 0′ with 0 then there is a degree b with b′ = 0′, bc = 0′ for every c, and ab for every a ˜ {0}. The proof is given as an oracle construction recursive in 0′. It follows that any nonrecursive degree below 0′ can be joined to 0′ by a degree strictly below 0′. Also, if a < 0′ and a″ = 0″ then there is a degree b such that ab = 0′ and ab = 0.