Tall cardinals in extender models

Gabriel Fernandes, Ralf Schindler

Research output: Contribution to journalArticlepeer-review


Assuming that there is no inner model with a Woodin cardinal, we obtain a characterization of λ-tall cardinals in extender models that are iterable. In particular, we prove that in such extender models, a cardinal κ is a tall cardinal if and only if it is either a strong cardinal or a measurable limit of strong cardinals.

Original languageEnglish
Pages (from-to)425-454
Number of pages30
JournalNotre Dame Journal of Formal Logic
Issue number3
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 by University of Notre Dame.


  • Core model
  • Extender models
  • Strong cardinals
  • Tall cardinals


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