A Uniqueness Theorem for Iterations

@article{Larson2002AUT,
  title={A Uniqueness Theorem for Iterations},
  author={Per-{\AA}ke Larson},
  journal={J. Symb. Log.},
  year={2002},
  volume={67},
  pages={1344-1350}
}
If M is a countable transitive model of ZFC+MAt1, then for every real x there is a unique shortest iteration j: M --+ N with x E N, or none at all. The fundamental construction underlying Woodin's I,,ax forcing [4] is the iterated generic elementary embedding. In this construction, one takes a countable transitive model M of ZFC, chooses an M-generic filter G c (9(ol)/INs)M (where INS denotes the nonstationary ideal) and constructs the corresponding ultrapower of M, with its associated… CONTINUE READING