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We show that if ℱ is a hereditary family of subsets of ${\omega }^{\omega }$ satisfying certain definable conditions, then the ${\Delta }_1^1$ reals are precisely the reals α such that $\beta :\alpha \in {\Delta }_1^1\left(\beta \right)\notin \in ℱ$. This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the $Q_{2n+1}$-encodable reals is also shown.