12 problems

Let $X$ be a set, let $\operatorname{\mathscr{L}}$ be a language, and let $\kappa$ be the relevant cardinal. Let $\AgeK$ be a non-trivial strong Fraïssé class, and let…

Let $\AgeK$ be a strong Fraïssé class satisfying $n$-DAP for every $n$ and having only countably many isomorphism types, where $n$-DAP is the disjoint $n$-amalgamation property. Le…

Let $\operatorname{\mathscr{L}}$ be a language, let $X$ be a set, and let $\kappa$ be the relevant cardinal. Let $\AgeK$ be a strong Fraïssé class in $\operatorname{\mathscr{L}}$,…

Let $X$ be the underlying set and let $\AgeK_0$ and $\AgeK_1$ be non-trivial Fraïssé classes, each with at most $|X|$ many elements up to isomorphism. Write $\CohenX$ for the Cohen…

Very canonical point-Ramsey conjecture. For every Fraïssé class, the very canonical point-Ramsey property is equivalent to the finite sunflower property.

Canonical point-Ramsey conjecture. For every Fraïssé class, the canonical point-Ramsey property is equivalent to the finite sunflower property.

Let $M$ be a Fraïssé structure. The new method of constructing faithful actions on structures isomorphic to $M$ should be applicable more generally to show universality of…

Let $\mathcal{K}$ be a relational Fraïssé class with strong amalgamation. The canonical vertex-Ramsey characterization. … The source also conjectures that having the finite $2$-sun…

Let $\mathcal{L}$ be a finite relational language, let $\mathcal{F}$ be a finite collection of finite irreducible $\mathcal{L}$-structures, and let…

Let $\mathcal{L}$ be a finite language, let $\mathcal{F}$ be an infinite collection of finite irreducible $\mathcal{L}$-structures such that no member of $\mathcal{F}$ embeds into…

Let $\mathcal{K}$ be a relational Fraïssé class with finitely many relations and a finite constraint set. Suppose that $\mathcal{K}$ satisfies the Ramsey property or has finite sma…

Let $\mathcal{K}$ be a relational Fraïssé class with finitely many relations and a finite constraint set. A constraint set is a finite set of finite structures such that membership…