有限结构的描述复杂性：保留量词秩
Descriptive Complexity of Finite Structures: Saving the Quantifier Rank
摘要：
给定一个n元关系结构M，设D（M）是在n元结构类中标识M直到同构的一阶公式的最小量词秩。明显的上界是D（M）\le n。证明了如果M中的关系的元数至多为k，则D（M）<（1- \frac{1}{2k}）n+k^2-k+2. n处的系数等于1- \frac{1}{2k}，可能不是最好的可能，但这是第一个已知的严格低于1的界限（对于固定的k）。如果一个人满足于具有更差的系数1- \frac{1}{2k^2+2}，那么他可以选择一个非常特殊形式的识别公式：至多有一个量词交替的前束公式。在这方面的其他一些结果。
英文摘要：
Given a relational structure M on n elements, let D(M) be the minimum quantifier rank of a first order formula identifying M up to isomorphism in the class of n-element structures. The obvious upper bound is D(M)\le n. We show that if the relations in M have arity at most k, then D(M)<(1-\frac{1}{2k})n+k^2-k+2. The coefficient at n, which equals 1-\frac{1}{2k}, is probably not best possible but this is the first known bound having it strictly below 1 (for fixed k). If one is content to have the worse coefficient 1-\frac{1}{2k^2+2}, then one can choose an identifying formula of a very special form: a prenex formula with at most one quantifier alternation. A few other results in this vein are presented.
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