  We present a new proof of the existence of Morley sequences in simple
theories. We avoid using the Erd\H{o}s-Rado theorem and instead use only
Ramsey's theorem and compactness. The proof shows that the basic theory of
forking in simple theories can be developed using only principles from
"ordinary mathematics", answering a question of Grossberg, Iovino and Lessmann,
as well as a question of Baldwin.
