## Proper forcings and absoluteness in $$L(\mathbb R)$$.(English)Zbl 0939.03054

Summary: We show that in the presence of large cardinals proper forcings do not change the theory of $${L({\mathbb R})}$$ with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.

### MSC:

 3e+55 Large cardinals 3e+40 Other aspects of forcing and Boolean-valued models

### Keywords:

proper forcing; large cardinals
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