Stably Measurable Cardinals

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We define a weak iterability notion that is sufficient for a number of arguments concerning Σ_1-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second uniform indiscernible for bounded subsets of kappa : u_2(kappa ), and secondly to give the consistency strength of a property of Lücke’s.
Original languageEnglish
Pages (from-to)448 - 470
Number of pages22
JournalJournal of Symbolic Logic
Issue number2
Early online date15 Jun 2020
Publication statusE-pub ahead of print - 15 Jun 2020


  • inner model
  • large cardinals
  • reflection principle


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