  We work with symmetric extensions based on L\'{e}vy Collapse and extend a few
results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her
P.h.d. thesis. We also observe that if $V$ is a model of ZFC, then
$DC_{<\kappa}$ can be preserved in the symmetric extension of $V$ in terms of
symmetric system $\langle \mathbb{P},\mathcal{G},\mathcal{F}\rangle$, if
$\mathbb{P}$ is $\kappa$-distributive and $\mathcal{F}$ is $\kappa$-complete.
Further we observe that if $V$ is a model of ZF + $DC_{\kappa}$, then
$DC_{<\kappa}$ can be preserved in the symmetric extension of $V$ in terms of
symmetric system $\langle \mathbb{P},\mathcal{G},\mathcal{F}\rangle$, if
$\mathbb{P}$ is $\kappa$-strategically closed and $\mathcal{F}$ is
$\kappa$-complete.
