Displaying similar documents to “The axiom of determinateness implies ω 2 has precisely two countably complete, uniform, weakly normal ultrafilters”

Proper forcings and absoluteness in L ( ℝ )

Itay Neeman, Jindřich Zapletal (1998)

Commentationes Mathematicae Universitatis Carolinae

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We show that in the presence of large cardinals proper forcings do not change the theory of L ( 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.