4 problems

For a graph class $\mathcal{C}$, say that it has bounded merge-width when its merge-width is bounded by a constant. A first-order transduction is an interpretation of graphs from s…

Let $0\leq d<\frac{1}{2}$, and let $\psi$ be a first-order sentence in the language of groups. Let $F_k$ be the free group of rank $k\geq 2$, and consider the density-$d$ random-gr…

Disjunctive-binding decidability conjecture. The fragment $db$ enjoys a decidable satisfiability problem.

Conjunctive-binding positive-properties conjecture. The fragment $cb$ enjoys the finite-model property and has a decidable satisfiability problem.