  We prove that after adding a Silver real no ultrafilter from the ground model
can be extended to a P-point, and this remains to be the case in any further
extension which has the Sacks property. We conclude that there are no P-points
in the Silver model. In particular, it is possible to construct a model without
P-points by iterating Borel partial orders. This answers a question of Michael
Hru\v{s}\'ak. We also show that the same argument can be used for the
side-by-side product of Silver forcing. This provides a model without P-points
with the continuum arbitrary large, answering a question of Wolfgang Wohofsky.
