Models of non-well-founded sets via an indexed final coalgebra theorem.

B. van den Berg, F. de Marchi

Research output: Contribution to journalArticleAcademicpeer-review


The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the chosen axiomatisation for the class of small maps.
Original languageEnglish
Pages (from-to)767-791
Number of pages25
JournalJournal of Symbolic Logic
Issue number3
Publication statusPublished - 2007


  • Other mathematical specialities
  • Wiskunde en computerwetenschappen
  • Wiskunde: algemeen


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