  We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$
by showing that for any set $C$ not of PA-degree and any set $A$, there exists
an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not
of PA-degree.
