Introduction to Forcing

Abstract

In proving that AC and GCH are consistent with ZF, Gödel used the so called method of internal models. From the assumption that the universe V is a model of ZF Gödel prescribed a method for producing a submodel L that is also a model of V = L, AC and GCH. This submodel is defined as the class of all sets having a certain property, i.e.,

$$ L = \left\{ {x\left| {\left( {\exists \alpha } \right)\left[ {x = F'\alpha } \right]} \right|} \right\} $$

.