一句话：研究有理数基 p/q 的可识别集合：给出一阶逻辑刻画，并证明自然序与模 q 运算不可识别。
设 p/q 为有理数，基 p/q 的计数系统用求值函数将 A_p={0,1,...,p-1} 上的有限词映射为有理数，其像记为 N_{p/q}。既有文献多关注求值为非负整数的词集，该语言相当混乱且非上下文无关。本文转而研究 (N_{p/q})^d 中由 (A_p)^d 上的有限自动机实现的 p/q-可识别子集。作者首先给出这类集合的一阶逻辑可定义性刻画，类似整数基计数系统中的 Büchi-Bruyère 定理；随后证明自然序关系与模 q 算子都不是 p/q-可识别的。
Let p/q be a rational number. Numeration in base p/q is defined by a function that evaluates each finite word over A_p={0,1,...,p-1} to some rational number. We let N_p/q denote the image of this evaluation function. In particular, N_p/q contains all nonnegative integers and the literature on base p/q usually focuses on the set of words that are evaluated to nonnegative integers; it is a rather chaotic language which is not context-free. On the contrary, we study here the subsets of (N_p/q)^d that are p/q-recognisable, i.e. realised by finite automata over (A_p)^d. First, we give a characterisation of these sets as those definable in a first-order logic, similar to the one given by the B\"uchi-Bruy\`ere Theorem for integer bases numeration systems. Second, we show that the natural order relation and the modulo-q operator are not p/q-recognisable.