# Folkman's theorem

Folkman's theorem (sets version): If $[2]^n$ is partitioned into c color classes, and n is sufficiently large depending on c, m, then one of the color classes contains all the strings in a m-dimensional combinatorial subspace containing at least one 1, where none of the fixed digits are equal to 1.
Folkman's theorem (integer version): If $[N]$ is partitioned into c color classes, and N is sufficiently large depending on c, m, then one of the color classes contains all the non-zero finite sums of an m-element set of positive integers.