< [[nlab:Sandbox]] Does LPO imply the following statement: > Let $\Sigma$ be the initial $\sigma$-frame. For any set $A$, any entire $\Sigma$-open relation $R:A \times \mathbb{2} \to \Sigma$ from $A$ to the boolean domain contains a functional entire relation, i.e. there exists a function $f:A \to \mathbb{2}$ such that for all $x$ in $A$ $R(x, f(x)) = \top$. [[!redirects Sandbox > history]]