Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

In 1948 Miroslav Katětov showed that if the cube X3 of a compact space X satisfies the separation axiom T5 then X must be metrizable. He asked whether X3 can be replaced by X2 in this metrization result. In this note we prove the consistency of this implication.

Newcomb’s problem is a decision puzzle whose difficulty and interest stem from the fact that the possible outcomes are probabilistically dependent on, yet causally independent of, the agent’s options. The problem is named for its inventor, the physicist William Newcomb, but first appeared in print in a 1969 paper by Robert Nozick [12]. Closely related to, though less well-known than, the Prison...