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Beginning Inner Model Theory

In: Handbook of Set Theory

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  • William J. Mitchell

    (University of Florida, Department of Mathematics)

Abstract

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.

Suggested Citation

  • William J. Mitchell, 2010. "Beginning Inner Model Theory," Springer Books, in: Matthew Foreman & Akihiro Kanamori (ed.), Handbook of Set Theory, chapter 17, pages 1449-1495, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-5764-9_18
    DOI: 10.1007/978-1-4020-5764-9_18
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