Itay Neeman and Jindrich
Zapletal
Abstract:
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 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
cardinals needed correspond to
the consistency strength of
${AD}^{L({\mathbb R})}$; roughly
$\omega$ Woodin cardinals.