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Published 1998 | In Press
Journal Article Open

Proper forcings and absoluteness in $L(\Bbb R)$

Abstract

We show that in the presence of large cardinals proper forcings do not change the theory of ${L({\Bbb R})}$ 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.

Additional Information

Received June 3, 1997, revised October 1, 1997. The second author acknowledges support from NSF grant DMS 9022140, GACR grant 201/97/0216 and CRM, Universita Autonoma de Barcelona.

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