{"schema":"vela.problem-packet.v0.1","problem":847,"statement":"Let $A\\subset \\mathbb{N}$ be an infinite set for which there exists some $\\epsilon>0$ such that in any subset of $A$ of size $n$ there is a subset of size at least $\\epsilon n$ which contains no three-term arithmetic progression.Is it true that $A$ is the union of a finite number of sets which contain no three-term arithmetic progression?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}