Abstract
Abstract This article explores computable reducibility for presentations of computable linear orders. In particular, this paper investigates the degree structures $\mathbf{P}(\mathcal{L})$ consisting of the $c$-degrees of computable copies of a fixed linear order $\mathcal{L}$, where $\mathcal{L}$ is one of the following: $\omega \cdot k$, $\omega ^{2}$, $\omega +\omega ^{*}$, $\zeta $ or $\omega \cdot \eta $. The main objective is to identify structural differences between these posets, focusing on the existence of least degrees, minimal degrees, universal degrees, minimal covers and the possible number of such covers. Among the notable differences, the structure $\mathbf{P}(\zeta )$ contains degrees with a minimal cover that is not a strong minimal cover, a phenomenon that does not occur in $\mathbf{P}(\omega )$.