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September 2007 Models of non-well-founded sets via an indexed final coalgebra theorem
Federico De Marchi, Benno van den Berg
J. Symbolic Logic 72(3): 767-791 (September 2007). DOI: 10.2178/jsl/1191333841

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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Federico De Marchi. Benno van den Berg. "Models of non-well-founded sets via an indexed final coalgebra theorem." J. Symbolic Logic 72 (3) 767 - 791, September 2007. https://doi.org/10.2178/jsl/1191333841

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

zbMATH: 1124.03049
MathSciNet: MR2354900
Digital Object Identifier: 10.2178/jsl/1191333841

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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