Arithmetic Progressions in Abundance by Combinatorial Tools
  Using the algebraic structure of the Stone-Cech compactification of the integers, Furstenberg and Glasner proved that for arbitrary k, every piecewise syndetic set contains a piecewise syndetic set of k-term arithmetic progressions.   We present a purely combinatorial argument which allows to derive this result directly from van der Waerden's Theorem. 
Mathias Beiglboeck