Conservative Extension

A conservative extension $\mathbb{T}_{2}$ of a Theory $\mathbb{T}_{1}$ is a Theory Extension $\mathbb{T}_{2}\to\mathbb{T}_{1}$ if every theorem of $\mathbb{T}_{1}$ is a theorem of $\mathbb{T}_{2}$, and every theorem of $\mathbb{T}_{2}$ expressible in the language of $\mathbb{T}_{1}$ is also a theorem of $\mathbb{T}_{1}$.