Paper: Elementary Axioms for Categories of Classes (at LICS 1999)
Authors: Alex K. SimpsonAbstract
We axiomatize a notion of "classic structure" on a regular category, isolating the essential properties of the category of classes together with its full subcategory of sets. Like the axioms for a topos, our axiomatization is very simple, but has powerful consequences. In particular, we show that our axiomatized categories provide a sound and complete class of models for Intuitionistic Zermelo-Fraenkel set theory.
BibTeX
@InProceedings{Simpson-ElementaryAxiomsfor, author = {Alex K. Simpson}, title = {Elementary Axioms for Categories of Classes}, booktitle = {Proceedings of the Fourteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 1999}, year = 1999, editor = {Giuseppe Longo}, month = {July}, pages = {77--85}, location = {Trento, Italy}, publisher = {IEEE Computer Society Press} }