7 problems

Pouzet's conjecture. Every $\omega$-well structured relational structure $\mathcal{A}$ is a reduct of an $\omega$-well structured, totally ordered structure.

Let $\mu$ be a finite relational signature, and let $\mathscr S_{\mu}$ be the class of all relational structures of signature $\mu$ without any finite monomorphic decomposition. A…

Let $R$ be a relational structure with a finite monomorphic decomposition, and let siblings be counted up to isomorphism. Finite monomorphic decomposition conjecture. Under this as…

Let $\mathcal{M}$ be an age-inexhaustible relational structure, meaning that any two finite substructures of $\mathcal{M}$ have disjoint copies within $\mathcal{M}$. Let the Camero…

Quasi-polynomiality conjecture. If $\varphi_R$ is bounded by some polynomial, then $\varphi_R$ is eventually a quasi-polynomial.

Equivalence conjecture. Any two regular relational symplectic groupoids integrating $M$ are equivalent.

Let $R$ be a relational structure with profile $\varphi_R$. Assume that $R$ has bounded signature or finite kernel, and that $\varphi_R(n)$ is bounded by some polynomial in $n$. Ev…