%0 Journal Article %T Natural Internal Forcing Schemata Extending ZFC %A Garvin Melles %J Mathematics %D 1993 %I arXiv %X Let V be the universe of sets and V_{\alpha} the sets of rank \leq\alpha. 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_{\alpha} %U http://arxiv.org/abs/math/9304202v1