Slicewise definability in first-order logic with bounded quantifier rank

Yijia Chen, Joerg Flum, Xuangui Huang

For every $q\in \mathbb{N}$ let ${\text{FO}}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{…