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Quotients of decidable objects in a topos

Published online by Cambridge University Press:  24 October 2008

Peter T. Johnstone
Peter T. Johnstone
Affiliation:
University of Cambridge
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Extract

In (5), Peter Freyd recently raised the question of whether every Grothendieck topos could be obtained from the topos of sets by means of the two constructions of taking sheaves on a locale and of taking continuous actions of a topological group (i.e. the topos-theoretic analogues of the set-theorists' techniques of forcing extensions and permutation models). He showed that these two constructions do suffice to within epsilon; provided we allow ourselves the freedom to take exponential varieties (4) (which do not change the internal logic of the topos) we can obtain every Grothendieck topos in this way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 409 - 419
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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