On infinite sets with no $3$ on a line
Abstract
We give a construction of an infinite set of points $A$ in $\mathbb{R}^2$ such that any subset $P\subseteq A$ has a constant density subset $P'$ with no three points collinear and yet $A$ cannot be separated into finitely many subsets such that each subset has no three points collinear. This provides a new proof of a question of Erdős, Nešetřil, and Rödl. The construction was generated by an internal model at OpenAI.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Topology and Set Theory
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 24 February 2026
- Language
- EN
- Document type
- Preprint