Abstract
In order to prove the independence of the Axiom of Choice from the axioms of ZF we cannot use the models which were employed in the previous section, since if M is a model of ZF + AC and G is P-generic over M, then M [G] also satisfies the AC. Yet the model N which we shall construct and which violates the AC is of the form M [G]. The corresponding language will have countably many symbols and we shall add to M countably many generic sets together with a set containing all these generic sets.
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