3 problems

Let $\alpha$ be as in the source, and let an invariant set mean a set closed under addition and multiplication. Countable invariant decomposition conjecture. If the proposed constr…

Let $\alpha$ be as in the source, and let a proper $k$-decomposition mean a decomposition into $k$ nonempty sets closed under addition and multiplication. Write $H_+$, $H_0$, and…

Let a finite decomposition of the positive elements of a field be given, and regard its pieces as ${\mathbb Q}$-convex sets. A separating hyperplane is a hyperplane separating piec…