Beginning Inner Model Theory

William J. Mitchell ()
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William J. Mitchell: University of Florida, Department of Mathematics

Chapter 17 in Handbook of Set Theory, 2010, pp 1449-1495 from Springer

Abstract: 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.

Keywords: Core Model; Large Cardinal; Measurable Cardinal; Force Notion; Proper Class (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4020-5764-9_18

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