ABSTRACT
This chapter presents Gödel's constructible universe. Starting with a ZF-universe V, the set of X-constructible sets for a given non-empty set X is defined, and the hierarchy of constructible sets of V is then also defined. This first part of the chapter ends with the proof that the universe L of the constructible sets of V is a ZF-universe.
The second part contains two results that have a crucial role in the metatheoretical independence proofs, which are the main topic in this part of the book. First, it is proved that L is a ZFC-universe and this entails that the axiom of choice is consistent with the ZF-theory. Then, by making essential use of the results of the preceding chapter, it is shown that the continuum hypothesis CH holds in the universe L; again, this has the consequence that CH is consistent with the ZFC-axioms.
