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On toposes generated by cardinal finite objects

Published online by Cambridge University Press:  23 May 2017

SIMON HENRY
SIMON HENRY*
Affiliation:
College de France, 3 Rue d'Ulm 75005 Paris, France. e-mail: henry@phare.normalesup.org
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Abstract

We give a characterisations of toposes which admit a generating set of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of “topological” conditions. The central result is that, constructively, a hyperconnected separated locally decidable topos admit a generating set of cardinal finite objects. The main theorem is then a generalisation obtained as an application of this result internally in the localic reflection of an arbitrary topos: a topos is generated by cardinal finite objects if and only if it is separated, locally decidable, and its localic reflection is zero dimensional.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 2 , September 2018 , pp. 209 - 223
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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