  In this article, we give two proofs of Carlson's theorem for located words
in~$\mathsf{ACA}^+_0$. The first proof is purely combinatorial, in the style of
Towsner's proof of Hindman's theorem. The second uses topological dynamics to
show that an iterated version of Hindman's theorem for bounded sums implies
Carlson's theorem for located words.
