A Basis Theorem for Perfect Sets

Marcia J. Groszek, Theodore A. Slaman
1998 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.
doi:10.2307/421023 fatcat:2aiqzu6k3ndotikgicphar2t34