4 problems

Let $K$ be a field, let $P_\alpha$ denote the principal series of order type $\omega^\alpha$, and let $R_\alpha$ denote the corresponding set of products of principal series appear…

Let $K$ be a field and let $b\in K((\mathbb{R}^{\leq 0}))$ be a random generalized power series, meaning that either $\operatorname{cl}(\operatorname{supp}(b))-\{0\}$ is…

Let $K((\mathbb{R}^{\leq 0}))$ be the ring of generalized power series, let $J$ be the germ ideal, and let $v_J$ denote the order-value. A series $a\in K((\mathbb{R}^{\leq 0}))$ is…

Let $K((\mathbb{R}^{\leq 0}))$ be the ring of generalized power series with exponents in $\mathbb{R}^{\leq 0}$. For a factorisation $a=b_1\cdot\ldots\cdot b_n$, a refinement is a f…