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

Published online by Cambridge University Press:  12 March 2014

Benno van den Berg  and
Federico de Marchi
Benno van den Berg
Affiliation:
Technische Universität Darmstadt, Fachbereich Mathematik, Schlobgartenstr. 7. 64289 Darmstadt, Germany. E-mail: berg@mathematik.tu-darmstadt.de.
Federico de Marchi
Affiliation:
Corso montegrappa 18/4, 16137 Genova, Italy. E-mail: feddem@libero.it
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 767 - 791
Copyright
Copyright © Association for Symbolic Logic 2007

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