An Outline of Inner Model Theory

John R. Steel ()
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John R. Steel: University of California at Berkeley, Department of Mathematics

Chapter 19 in Handbook of Set Theory, 2010, pp 1595-1684 from Springer

Abstract: 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.

Keywords: Initial Segment; Direct Limit; Iteration Strategy; Canonical Embedding; Successor Cardinal (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-5764-9_20

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DOI: 10.1007/978-1-4020-5764-9_20

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