Relating first-order set theories and elementary toposes

Bulletin of Symbolic Logic 13 (3):340-358 (2007)
We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo—Fraenkel set theory (IZF)
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/4493324
 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: 15,879
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

No references found.

Add more references

Citations of this work BETA
Nathanael Leedom Ackerman (2010). Relativized Grothendieck topoi. Annals of Pure and Applied Logic 161 (10):1299-1312.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

31 ( #101,145 of 1,725,168 )

Recent downloads (6 months)

3 ( #210,933 of 1,725,168 )

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.