feat(ErdosProblems): 847

[archiebrowne]

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?

Closes #973

[Paul-Lez]

Let's give this a slightly more suggestive name, e.g. HasFew3APs (happy to hear better suggestions:))

Adding a docstring would also be useful for readability.