7 problems

A countable signature $\sigma$ and a class $\mathscr C$ of $\sigma$-structures are given. A unary expansion of $\mathscr C$ is obtained by adding unary relation symbols. Monadic NI…

Strong modeling limit conjecture. Every FO-convergent sequence of graphs in $\mathscr C$ has a strong modeling FO-limit. The paper proves existence of modeling FO-limits for monadi…

Let $\mathbf L$ be a tree-modeling, meaning a modeling whose underlying structure is a tree, and suppose that it satisfies the Strong Finitary Mass Transport Principle. Assume also…

The residual modeling-limit conjecture. Every first-order-convergent residual sequence admits a modeling first-order limit. By the results preceding the conjecture, this is equival…

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…

Let a modeling be a measurable graph equipped with a probability measure for which first-order definable sets are measurable. A graph has bounded degree if its vertex degrees are u…

Let $(G_n)_{n\in\mathbb{N}}$ be an FO-convergent sequence of graphs, and suppose that the class $\{G_n:n\in\mathbb{N}\}$ is nowhere dense. Nowhere-dense modeling FO-limit conjectur…