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Models of Non-Well-Founded Sets via an Indexed Final Coalgebra Theorem

Benno Van Den Berg and Federico De Marchi
The Journal of Symbolic Logic
Vol. 72, No. 3 (Sep., 2007), pp. 767-791
Stable URL: http://www.jstor.org/stable/27588570
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Models of Non-Well-Founded Sets via an Indexed Final Coalgebra Theorem
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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.

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