Erdős Problem 589

### What is the conjecture

https://www.erdosproblems.com/589

Let $g(n)$ be maximal such that in any set of $n$ points in $\mathbb{R}^2$ with no four points on a line there exists a subset on $g(n)$ points with no three points on a line. Estimate $g(n)$.

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading the linked Erdős Problems page for Problem 589 and then inspect existing formalized conjectures in the repository for conventions and structure. Done means the stated conjecture has been added to the collection with a faithful formal statement and any required validation passes.

Written by the indexing model from the issue text.