Summary: This chapter provides an introduction to the basic theory of inner models of set theory, without fine structure. Section 1 begins with the basic theory of Gödel’s class \(L\) of constructible sets, with an emphasis on the condensation property, introduces sharps, and includes a brief discussion of the Dodd-Jensen core model. The next two sections describe the extension of these concepts to arbitrary sequences of measures, and then via extender models to cardinal properties stronger than measurability. Section 4 gives a summary of the status and known properties of inner models for cardinals ranging from strong to supercompact, and the final section discusses core models.
See also the review of the complete volume [Zbl 1197.03001].
For the entire collection see [Zbl 1197.03001].