In this answer it is stated that in William Reinhardt's paper 'Remarks on reflection principles, large cardinals, and elementary embeddings' (1974)
Reinhardt suggests extending the set-theoretic universe beyond $V_\Omega$ (where $\Omega$ denotes the class of ordinals) to some "virtual realm" of larger objects: $V_{\Omega+1}$, $V_{\Omega+\Omega}$, and so on.
I have not been able to find a free copy of the paper & was wondering if someone could elaborate on the method Reinhardt suggests.
Additionally:
- Does this method have a name?
- What is the upper limit of this method?
Any additional online references for further reading would also be greatly appreciated.