6 problems

Let $A$ be a set and let $\rho$ be a partial order on $A$ with least element $0$ and greatest element $1$. Let $\operatorname{Pol}\rho$ be the clone of operations preserving $\rho$…

Let $\mathsf{MA}(\sigma\text{-centered})$ hold, and let $(P,<)$ be a partial order of size at most $2^{\mathfrak{c}}$ such that every $p\text{in}P$ has at most $\mathfrak{c}$ many p…

Let $k\geq 2$, and let $W_n$ be a set of $n$ random intervals. Write $E[k\operatorname{-wd}(W_n)]$ for the expected $k$-width of $W_n$. Random-interval set scaling conjecture. Ther…

Let $k\geq 2$, and let $R_n$ be a sequence of $n$ random intervals. Write $E[k\operatorname{-wd}(R_n)]$ for the expected $k$-width of $R_n$. Random-interval sequence scaling conjec…

Three sporadic entropic-order conjectures. The following three relations hold:

Let $G$ be the Hermitian Lie group considered above, with maximal bi-invariant order, maximal continuous bi-invariant order, and, when $G$ is of tube type, geometric order. Coincid…