14 problems

A binary relational structure is a relational structure whose relations have arity at most two. Milliken's theorem conjecture. Aside from Ramsey's theorem itself, Milliken's theore…

Let $L$ be a relational language with finitely many unary relations and infinitely many relations of some arity $a\geq 2$. Let $\str H$ be a countable unrestricted $L$-structure re…

Let $\str H$ and $\str G$ be the structures in the source, let $\varphi\colon\str H\to\str G$ be an embedding, and let an envelope of a finite subset have the source's valuation-tr…

Let $\sigma$ be the sequence recording the numbers of relations of the relevant arities, and let $\str H\to\str G$ be an embedding equipped with the notion of $k$-enveloping from t…

Let $\str H$ and $\str G$ be the structures and let $k$-enveloping embeddings be as defined in the source. When the number of relations increases with arity, a nonexistence conject…

Let $L$ be a relational language with finitely many relations of every arity greater than one and finitely many unary relations, and let $\str H$ be a countable unrestricted $L$-st…

For $n\geq 3$, let $\mathcal{M}_n$ be the class of finite metric spaces whose distances lie in ${1,\ldots,n}$, and let $\mathbf{M}_n=\operatorname{Flim}(\mathcal{M}_n)$ be its Fraï…

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 $k$-clique-free graphs be graphs containing no complete subgraph on $k$ vertices, with the triangle-free case corresponding to $k=3$. Big Ramsey degrees measure the least numbe…

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…

Let $d4a4_k$ be the countable universal homogeneous $k$-clique-free graph, and let $d4a2$ be a finite $k$-clique-free graph. Suppose that the currently missing lower bounds for the…

Let $d4a4_k$ be the countable universal homogeneous $k$-clique-free graph, and let $d4a2$ be a finite $k$-clique-free graph. An incremental antichain of coding nodes is an antichai…

Conjecture on lower bounds and Zucker's conditions. Once found, the lower bounds will satisfy the conditions needed for Zucker's work to apply.