Separating principles below Ramsey's Theorem for Pairs

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from $\text{RT}$, Ramsey’s Theorem for Pairs. These principles tend to fall outside of the “big five” systems of reverse mathematics and a complicated picture of subsystems below $\text{RT}$ has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that $\text{ADS}$ is not equivalent to $\text{CAC}$ and that $\text{EM}$ is not equivalent to $\text{RT}$.