I need to show that the Well Ordering principle which is $(\forall X)(\exists R) [(X, R )$ - a well ordered set$]$
is true in $H(\kappa)$ where
$H(\kappa)$ is hereditary set of $\kappa$ - infinite cardinal.
I know that Axiom of Choice is true in $H(\kappa)$, but not the Power Set Axiom, and I was also advised to use the following fact
$R$ is a well founded relation on X $\to$ $H(\kappa) \models $ “R is a well founded relation on X”
but I do not know how it helps, because in the original proof of WOP well roundedness is not used