3 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 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…