Infinite decreasing chains in the Mitchell order

Omer Ben-Neria, Sandra Müller*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. The purpose of the paper is to make a first step in understanding this case, by studying the extent to which the Mitchell order can be ill-founded. Our main results are (i) in the presence of a rank-to-rank extender there is a transitive Mitchell order decreasing sequence of extenders of any countable length, and (ii) there is no such sequence of length ω1.

Original languageAmerican English
Pages (from-to)771-781
Number of pages11
JournalArchive for Mathematical Logic
Issue number6
StatePublished - Aug 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).


  • Infinite decreasing chain
  • Mitchell order
  • Rank-to-rank extender


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