3 problems

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 $R$ be a relational structure, and let $\operatorname{sib}(R)$ denote the number of siblings of $R$, counted up to isomorphism. A structure is cellular in the sense used in the…

Finite basis conjecture. There is a finite subset $\mathfrak A$ of pairwise incomparable structures in $\mathscr S_{\mu}$ such that every member of $\mathscr S_{\mu}$ embeds some m…