Abstract
Abstract
Assuming
$\mathrm{PFA}$
, we shall use internally club
$\omega _1$
-guessing models as side conditions to show that for every tree T of height
$\omega _2$
without cofinal branches, there is a proper and
$\aleph _2$
-preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the
$\omega _1$
-approximation property.
Publisher
Cambridge University Press (CUP)