Problem 881

Erdős Problem #881: declared status 'open'. Formalized: yes. Let $A\subset\mathbb{N}$ be an additive basis of order $k$ which is minimal, in the sense that if $B\subset A$ is any infinite set then $A\backslash B$ is not a basis of order $k$. Must there exist an infinite $B\subset A$ such that $A\backslash B$ is a basis of order $k+1$? Prize: no. Tags: additive basis, number theory.