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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:

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