Bulletin of Symbolic Logic
We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M.
Groszek, Marcia J. and Slaman, Theodore A. A., "A Basis Theorem for Perfect Sets" (1998). Open Dartmouth: Faculty Open Access Articles. 2411.