一句话：定义有限随机结构的一阶复杂度层级，引入随机 FO 归约，给出若干新逻辑极限律并证明 0-1 律句法集不可递归枚举。
本文研究关系签名上 n 元素域随机结构序列的一阶逻辑极限行为。作者将 FO complexity 定义为 Banach 空间 ℓ∞/c0 的一个子集，指出经典的 FO 零一律与 FO 收敛律分别对应复杂度 {0,1} 和 R 的子集。论文建立 FO 复杂度类层级，引入 stochastic FO reduction，从而可在不同随机结构之间迁移复杂度结果，并借此得到二项随机结构的若干新逻辑极限律。最后，作者引入受 FO 句子 φ 约束的图条件分布，推广了若干著名随机图模型，为每个复杂度类给出实例，并证明满足 0-1 律的 φ 集合不是递归可枚举的。
For a sequence of random structures with n-element domains over a relational signature, we define its FO complexity as a certain subset in the Banach space ℓ∞/c0. The well-known FO zero-one law and FO convergence law correspond to FO complexities equal to {0, 1} and a subset of R, respectively. We present a hierarchy of FO complexity classes, introduce a stochastic FO reduction that allows to transfer complexity results between different random structures, and deduce using this tool several new logical limit laws for binomial random structures. Finally, we introduce a conditional distribution on graphs, subject to a FO sentence ϕ, that generalises certain well-known random graph models, show instances of this distribution for every complexity class, and prove that the set of all ϕ validating 0--1 law is not recursively enumerable.