Let M be a random set of integers greater than 1, containing each integer n independently with probability 1/n. Let S(M) be the sumset of M, that is, the set of all sums of subsets of M. How many independent copies of S must one intersect in order to obtain a finite set?

This problem is the limiting form of a problem arising in computational Galois theory. Dixon (1992) conjectured that O(1) was good enough, which was proved shortly thereafter by Luczak and Pyber. Their constant was 2^100 has not been improved until now, though is conjectured that it can be improved to 5 or 4. We show in fact that 4 sets suffice.

JOINT WORK WITH YUVAL PERES AND IGOR RIVIN