8 problems

Large-cardinal dimension-range conjecture. The appearance of large cardinal values in the functional representation of the dimension range of an espalier should be closely related…

Let $\mathcal{C}$ be a class of finite structures that is universally well-quasi-ordered. Consider adding a total order on the vertices of every structure in $\mathcal{C}$. Pouzet'…

Nešetřil's conjecture. All hereditary Ramsey classes of freely ordered hypergraphs had already been known earlier.

Let $\Delta^n=\{(x_1,\ldots,x_n)\in[0,1]^n: x_1\leq\cdots\leq x_n\}$, and let $F\subseteq\Delta^n$. Write $F^c=\Delta^n\setminus F$. The rank of a set is defined by the preceding r…

Let $\pi\in S_n$ be a permutation. A weak-twin of $\pi$ is a pair of disjoint index sets $I=\{i_1<\dots<i_\ell\}$ and $J=\{j_1<\dots<j_\ell\}\subset[n]$ such that … where…

Let $\mathscr C$ be an infinite class of finite ordered structures. Kolaitis's ordered conjecture. There is a sentence $\varphi\bin \text{\sf{LFP}}$ that is not equivalent on…

Let $\mathfrak D$ be a hereditary class of indecomposable ordered binary structures. Suppose that $\mathfrak D$ is hereditary well-quasi-ordered and hereditary algebraic. Sum-closu…

Let $\theta$ and $\mu$ be cardinals with $\mu>\theta$. Consider the partial order of functions ${}^{(\theta^{+3})}\mu$ ordered modulo the ideal $[\theta^{+3}]^{\leq\theta}$ of subs…