Gyula Karolyi: Ordering groups without long monotone arithmetic progressions

We study orderings and well-orderings of groups without
long monotone arithmetic progressions. For example we prove that every
commutative group has a well-ordering that does not contain a monotone
arithmetic progression of length 6. The starting point is the following answer to an old problem of Erdos: the real numbers can be ordered such a way that there is no 3-term monotone arithmetic progression. This is
a joint work with Peter Komjath.