We first prove a theorem about reals (subsets of $\mathbb{N}$) and classes of reals: If a real $X$ is $\Sigma_{1}^{1}$ in every member $G$ of a nonempty $\Sigma_{1}^{1}$ class $\mathcal{K}$ of reals then $X$ is itself $\Sigma _{1}^{1}$. We also explore the relationship between this theorem, various basis results in hyperarithmetic theory and omitting types theorems in several generalized and modal logics. We then prove the analog of our first theorem for classes of reals: If a class $\mathcal{A}$ of reals is $\Sigma_{1}^{1}$ in every member of a nonempty $\Sigma_{1}^{1}$ class $\mathcal{B}$ of reals then $\mathcal{A}$ is itself $\Sigma_{1}^{1}$.