The purpose is to study the strength of Ramsey's Theorem for pairs restricted
to recursive assignments of k-many colors, with respect to Intuitionistic
Heyting Arithmetic. We prove that for every natural number k≥2, Ramsey's
Theorem for pairs and recursive assignments of k colors is equivalent to the
Limited Lesser Principle of Omniscience for Σ30 formulas over Heyting
Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is
equivalent to: for every recursively enumerable infinite k-ary tree there is
some i<k and some branch with infinitely many children of index i.Comment: 17 page