Consider the satement
$\mathsf{RT}^{p}$ (Infinite Ramsey's Theorem for exponent $p\in\mathbb{N}$): For any $r\in\mathbb{N}$, and for any function $c:[\mathbb{N}]^{p}\rightarrow [r]$, there exists an infinite subset $A\subseteq \mathbb{N}$ such that $c|_{[A]^{p}}$ is constant.
Ramsey's Theorem for singletons is simple the statement $\mathsf{RT}^{1}$. On page 258 of the book- Reverse Mathematics: Problems, Reductions, and Proofs by Damir D. Dzhafarov & Carl Mummert- the following diagram illustrates the location of versions of Ramsey’s theorem below $\mathsf{ACA}^{'}$.
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There is something I do not understand regarding the meaning of the arrows in the diagram, and I cannot seem to clear it on my own: Given that $\mathsf{WKL}_{0}\Rightarrow\mathsf{RCA}_{0}+\mathsf{B\Sigma_{2}^{0}}$ and that $\mathsf{B\Sigma_{2}^{0}}\leftrightarrow\mathsf{RT}^{1}$, why is it not true that $\mathsf{WKL}_{0}\vdash\mathsf{RT}^{1}$, which I know not to be true (see Corollary 6.5, p.106 here: Combinatorics in Subsystems of Second Order Arithmetic, by J.L. Hirst - Ph.D. Thesis)?