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.


03E55 Large cardinals
03E40 Other aspects of forcing and Boolean-valued models
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