An introduction to generalized descriptive set theory, part 2

After introducing the notions of $\kappa$-Borel class, $\kappa$-$\Delta_1^1$ class, $\kappa$-Borel^* class in the previous talk ( http://u.math.biu.ac.il/~morenom3/GDST-2018.pdf ), in this talk, we will show the relation between this classes.
In descriptive set theory the Borel class, the $\Delta_1^1$ class, the Borel* class are the same class, this doesn't hold in the generalized descriptive set theory, in particular under the assumption V=L the Borel* class is equal to the $\Sigma1^ 1$ class.