Proper Forcing and L(r)

  title={Proper Forcing and L(r)},
  author={Itay Neeman and Jindrich Zapletal},
We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing; we show further that a set of ordinals in V cannot be added to L(R) by small forcing. The large cardinal needed corresponds to the consistency strength of ADL(R); roughly ω Woodin cardinals. 

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