In Inner Models with Woodin Cardinals

Sandra Müller, Grigor Sargsyan

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1 Scopus citations


We analyze the hereditarily ordinal definable sets in for a Turing cone of reals x, where is the canonical inner model with n Woodin cardinals build over x and g is generic over for the Lévy collapse up to its bottom inaccessible cardinal. We prove that assuming-determinacy, for a Turing cone of reals x, where is a direct limit of iterates of, is the least Woodin cardinal in, is the least inaccessible cardinal in above, and is a partial iteration strategy for. It will also be shown that under the same hypothesis satisfies.

Original languageEnglish (US)
Pages (from-to)871-896
Number of pages26
JournalJournal of Symbolic Logic
Issue number3
StatePublished - Sep 13 2021

All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic


  • HOD
  • Woodin cardinal
  • determinacy
  • inner model theory
  • large cardinal
  • mouse


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