Ramsey's theorem for pairs and K colors as a sub-classical principle of arithmetic

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 , Ramsey’s Theorem for pairs and recursive assignments of k colors is equivalent to the Limited Lesser Principle of Omniscience for 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 and some branch with infinitely many children of index i.