A note on Russell's paradox in locally cartesian closed categories

Studia Logica 48 (3):377 - 387 (1989)
Working in the fragment of Martin-Löfs extensional type theory [12] which has products (but not sums) of dependent types, we consider two additional assumptions: firstly, that there are (strong) equality types; and secondly, that there is a type which is universal in the sense that terms of that type name all types, up to isomorphism. For such a type theory, we give a version of Russell's paradox showing that each type possesses a closed term and (hence) that all terms of each type are provably equal. We consider the kind of category theoretic structure which corresponds to this kind of type theory and obtain a categorical version of the paradox. A special case of this result is the degeneracy of a locally cartesian closed category with a morphism which is generic in the sense that every other morphism in the category can be obtained from it via pullback.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF00370830
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 22,184
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

Add more references

Citations of this work BETA
Paul Taylor (1996). Intuitionistic Sets and Ordinals. Journal of Symbolic Logic 61 (3):705-744.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

28 ( #148,235 of 1,934,834 )

Recent downloads (6 months)

2 ( #270,038 of 1,934,834 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.