  $\Theta$-Hilbertianity and its strengthening, strong $\Theta$-Hilbertianity,
are two generalizations of Hilbertianity inspired by Jarden's definition of
$p$-Hilbertianity and strong $p$-Hilbertianity. Jarden has asked whether the
two notions defined by him are actually the same. We address this question in
its more general version of $\Theta$-Hilbertianity and show that for PRC, and,
in particular, for PAC fields, $p$-Hilbertianity and strong $p$-Hilbertianity
coincide.
