{"schema":"vela.problem-packet.v0.1","problem":623,"statement":"Let $X$ be a set of cardinality $\\aleph_\\omega$ and $f$ be a function from the finite subsets of $X$ to $X$ such that $f(A)\\not\\in A$ for all $A$. Must there exist an infinite $Y\\subseteq X$ that is independent - that is, for all finite $B\\subset Y$ we have $f(B)\\not\\in Y$?","status":"open","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)"}