The strength of Ramsey's theorem for pairs and arbitrarily many colors

In this paper, we show that ${\mathrm{R}\mathrm{T}}^2+{\mathsf{W}\mathsf{K}\mathsf{L}}_0$ is a ${\mathrm{\Pi }}_1^1$-conservative extension of $\mathrm{B}{\mathrm{\Sigma }}_3^0$.