4 problems

Let $\underline{M}$ be the class of orders generated from the one-point order by finite sums, products with $\omega$ and $\omega^*$, and the specified dense rational-indexed sums.…

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 $\mathfrak D$ 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…