We study the structure Ceprs induced by degrees of computably enumerable preorder relations with respect to computable reducibility ≤_c. It is proved that the structure of computably enumerable equivalence relations is definable in Ceprs. This fact and results of Andrews, Schweber, and Sorbi imply that the theory of the structure Ceprs is computably isomorphic to first-order arithmetic. It is shown that a Σ₁-fragment of the theory is decidable, while its Π₃-fragment is hereditarily undecidable. It is stated that any two incomparable degrees in Ceprs do not have a least upper bound, and that among minimal degrees in Ceprs, exactly two are c-degrees of computably enumerable linear preorders.

我们研究了结构Ceprs相对于可计算还原≤诱导度computably枚举序关系_Ç。证明了可计算的等价关系的结构在Ceprs中是可以定义的。Andrews，Schweber和Sorbi的事实和结果表明，结构Ceprs的理论与一阶算术是可计算同构的。结果表明，一个Σ ₁理论的-Fragment是可判定的，而它的Π ₃ -Fragment是遗传判定的。有人指出，在塞普尔（Cerprs）中，任何两个无可比拟的度数都没有最小上界，而在塞普尔（Cerprs）中的最小度数中没有上限。，恰好两个是c级可计算的线性预排序。