Proper forcing and absoluteness in L(R)

 

Itay Neeman and Jindrich Zapletal

 

 

Abstract:

 

We show that in the presence of large cardinals proper

forcings do not change the theory of $L({\mathbb R})$

with reals 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.