Obtaining Woodin's cardinals

Philip D Welch*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

6 Citations (Scopus)
391 Downloads (Pure)


Since the 1980’s work on Projective Determinacy and ADL(R) the concept of Woodin cardinal has become to be seen as central in the theory of large cardinals and inner model theory. The use by Woodin himself of a background assumption in many arguments that the universe contains unboundedly many such cardinals again draws attention to the centrality of this concept.

As is well known the Reflection Principles dating to a more classicial era only provide large cardinals consistent with V = L, and not the wherewithal for such theorems on absoluteness under set forcing that Woodin has proven.

We discuss here a reflection principle derived from weak sub-compactness that implies the existence of a proper class of measurable Woodin cardinals - thus providing adequate background assumptions for many of Woodin’s absoluteness results in his work
Original languageEnglish
Title of host publicationFoundations of Mathematics
Subtitle of host publicationLogic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA
EditorsAndres Eduardo Caicedo, James Cummings, Peter Koellner, Paul B Larson
PublisherAmerican Mathematical Society
Number of pages16
ISBN (Electronic)9781470440794
ISBN (Print)9781470422561
Publication statusPublished - 30 May 2017

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Reflection
  • Woodin cardinals


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