Proper forcing and $L({\mathbb R})$

Details Proper forcing and $L({\mathbb R})$ Proper forcing and $L({\mathbb R})$

2000-03-03

arxiv.org/abs/math/0003027v1

Mathematics

Logic

14 pages, includes Appendix (pp. 10--13)

Scientific paper

We present two ways in which the model $L({\mathbb R})$ is canonical assuming the existence of large cardinals. We show that the theory of this model, with {\em ordinal} parameters, cannot be changed by small forcing; we show further that a set of ordinals in $V$ cannot be added to $L({\mathbb R})$ by small forcing. The large cardinal needed corresponds to the consistency strength of $AD^{L({\mathbb R})}$; roughly $\omega$ Woodin cardinals.

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