6 problems

Hereditary-discrepancy characterization. A monotone class $\mathscr{C}$ is nowhere dense if and only if, for every partitioned formula $\varphi(\bar{x};\bar{y})$, every…

Quantifier-elimination conjecture. The quantifier-elimination scheme involving unary relations and functions does not extend from classes of bounded expansion to the more general n…

Admissible-lift conjecture. Every local-global convergent sequence of graphs in a nowhere dense class has a modeling limit.

A sequence of finite structures may have a measurable limit representation on a standard probability space. Modeling representation conjecture. Every convergent sequence of graphs…

Structural conjecture for nowhere dense classes. If $\mathcal C$ does not have bounded expansion, then there exists an integer $p$ such that $\mathcal C$ includes $p$-subdivisions…

Let a monotone class of graphs be a class closed under taking subgraphs, and let it admit modeling limits when every first-order-convergent sequence from the class has a modeling l…