Iterated Forcing and Elementary Embeddings

James Cummings ()
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James Cummings: Carnegie Mellon University, Department of Mathematics

Chapter 12 in Handbook of Set Theory, 2010, pp 775-883 from Springer

Abstract: Abstract I give a survey of some forcing techniques which are useful in the study of large cardinals and elementary embeddings. The main theme is the problem of extending a (possibly generic) elementary embedding of the universe to a larger domain, which is typically a generic extension of the ground model by some iterated forcing construction. Topics covered include (a) building, transfer and alteration of generic objects (b) strong and weak master conditions (c) the use of guessing principles (d) term forcing (e) the Kunen, Levy, Mitchell and Silver collapses The techniques which I discuss are illustrated with many examples. These include the failure of GCH at a measurable cardinal, the consistency of PFA, the laver indestructibility theorem, and the existence of a saturated ideal on the least uncountable cardinal.

Keywords: Regular Cardinal; Measurable Cardinal; Transitive Model; Master Condition; Stationary Subset (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_13

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DOI: 10.1007/978-1-4020-5764-9_13

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