The Contiguity in R/M

An r.e. degree c is contiguous if degwtt(A)=degwtt(B) for any r.e. sets A, B ** c.In this paper, we generalize the notation of contiguity to the structure R/M, the upper semilattice of the r.e. degree set R modulo the cappable r.e. degree set M. An elementc ** R/M is contiguous if degwtt(A)=degwtt(B) for any r.e. sets A, B such that degT(A), degT(B)**c. It is proved in this paper that every nonzero element in R/M is not contiguous, I.e., for every element c**R/M, ifc !=o then there exist at least two r.e. setsA, B such that degT(A), degT(B)**c and degwtt(A)!=degwtt(B).