Infinite subsets of random sets of integers
  There is an infinite subset of a Martin-L\"of random set of integers that does not compute any Martin-L\"of random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-L\"of random set of integers, and apply a result of Miller. 
Bj{\o}rn Kjos-Hanssen
math.LO