A Hausdorff topological space X is van der Waerden if for every sequence
(x_n)_n in X there is a converging subsequence (x_n)_{n in A} where subset A of
omega contains arithmetic progressions of all finite lengths. A Hausdorff
topological space X is Hindman if for every sequence (x_n)_n in X there is an
IP-converging subsequence (x_n)_{n in FS(B)} for some infinite subset B of
omega. We show that the continuum hypothesis implies the existence of a van der
Waerden space which is not Hindman

Kojman, Menachem