Fourteenth Annual IEEE Symposium on

Logic in Computer Science (LICS 1999)

Paper: Elementary Axioms for Categories of Classes (at LICS 1999)

Authors: Alex K. Simpson


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.


    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}