Mathematics – Logic
Scientific paper
2009-12-07
Mathematics
Logic
Scientific paper
This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a "predicative category with small maps" which axiomatises the idea of a category of classes and class morphisms, together with a selected class of maps whose fibres are sets (in some axiomatic set theory). The main result of the present paper is that such predicative categories with small maps are stable under internal sheaves. We discuss the sheaf models of constructive set theory this leads to, as well as ideas for future work.
den Berg Benno van
Moerdijk Ieke
No associations
LandOfFree
Aspects of Predicative Algebraic Set Theory III: Sheaves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Aspects of Predicative Algebraic Set Theory III: Sheaves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Aspects of Predicative Algebraic Set Theory III: Sheaves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-243325