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
JournalJournal of Symbolic Logic
Publication statusAccepted/In press - 27 Nov 2019


  • inner model
  • large cardinals
  • reflection principle

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