Abstract
In this paper, we study the joint degree spectrum of the successor and the block relations on computable linear orders. The joint degree spectrum of relations \(R_{1},R_{2},\dots,R_{n}\) on a computable structure \(\mathcal{A}\) is the set of all Turing degrees \(\mathbf{x}\) such that there is a computable \(\mathcal{B}\cong\mathcal{A}\) and the degrees of all \(R_{i}(\mathcal{B})\) are the same and coincide with \(\mathbf{x}\) . We prove that the joint degree spectrum of the successor and the block relations on a computable non-trivial \(\eta\) -like linear order is closed upwards in c.e. degrees. Also we obtain some effective properties of the successor relation on computable linear orders.
