A lattice of definability subspaces in the order of rational numbers is described. It is proved that this lattice consists of five subspaces defined in the paper that are generated by the following relations: “equality,” “less,” “between,” “cycle,” and “linkage.” For each of the subspaces, its width (the minimum number of arguments of a generating relation) is found and a convenient description of the automorphism group is given. Although the structure of this lattice was known previously, the proof in the paper is of syntactic nature and avoids the use of a group-theoretical method.

中文翻译：

---

有理数阶可定义格

描述了一个按有理数顺序的可定义子空间格。证明该格由论文中定义的五个子空间组成，这些子空间由以下关系生成：“相等”、“较少”、“介于”、“循环”和“链接”。对于每个子空间，找到其宽度（生成关系的最小参数数）并给出自同构群的方便描述。虽然这个格的结构以前是已知的，但论文中的证明是句法性质的，避免使用群论方法。