  We adapt the construction of subsets of {1, 2, ..., N} that contain no k-term
arithmetic progressions to give a relatively thick subset of an arbitrary set
of N integers. Particular examples include a thick subset of {1, 4, 9, ...,
N^2} that does not contain a 3-term AP, and a positive relative density subset
of a random set (contained in {1, 2, ..., n} and having density c n^{-1/(k-1)})
that is free of k-term APs.
