Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proper forcing and $L({\mathbb R})$   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.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess