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An Outline of Inner Model Theory

In: Handbook of Set Theory

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  • John R. Steel

    (University of California at Berkeley, Department of Mathematics)

Abstract

This paper outlines the basic theory of canonical inner models satisfying large cardinal hypotheses. It begins with the definition of the models, and their fine structural analysis modulo iterability assumptions. It then outlines how to construct canonical inner models, and prove their iterability, in roughly the greatest generality in which it is currently known how to do this. The paper concludes with some applications: genericity iterations, proofs of generic absoluteness, and a proof that the hereditarily ordinal definable sets of L(ℝ) constitute a canonical inner model.

Suggested Citation

  • John R. Steel, 2010. "An Outline of Inner Model Theory," Springer Books, in: Matthew Foreman & Akihiro Kanamori (ed.), Handbook of Set Theory, chapter 19, pages 1595-1684, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-5764-9_20
    DOI: 10.1007/978-1-4020-5764-9_20
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