Natural Internal Forcing Schemata Extending ZFC
arXiv:math/9304202
Abstract
Let V be the universe of sets and V_α the sets of rank \leqα. We develop some axiom schemata for set theory based on the following three assumptions: 1. V \models ZFC 2. V is large with respect to the class of ordinals 3. V is large with respect to each of the V_α