Ramsey's theorem for computably enumerable colorings
Tamara Hummel, Carl G. Jockusch · Journal of Symbolic Logic · 2001
Abstract It is shown that for each computably enumerable set of n-element subsets of ω there is an infinite set A ⊆ ω such that either all n-element subsets of A are in or no n-element subsets of A are in . An analogous result is obtained with the requirement that A be replaced by the requirement that the jump of A be computable from 0(n). These results are best possible in various senses.