The contiguity in R/M
An r.e. degree c is contiguous if deg(wtt)(A) = deg(wtt)(B) for any r.e. sets A, B E 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 element [c] is an element of R/M is contiguous if [deg(wtt)(A)] = [deg(wtt)(B)] for any r. e. sets A, B such that deg(T)(A), deg(T)(B) is an element of [c]. It is proved in this paper that every nonzero element in R/M is not contiguous, i.e., for every element [c] is an element of R/M, if [c] not equal [o] then there exist at least two r.e. sets A, B such that deg(T)(A), deg(T)(B) is an element of [c] and [deg(wtt)(A)] not equal [deg(wtt)(B)].
contiguous turing degree recursively enumerable set