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

Authors: Alex K. Simpson

Abstract

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 Symposium on Logic in Computer Science (LICS 1999)},
    year =	 {1999},
    month =	 {July}, 
    pages =      {77--85},
    location =   {Trento, Italy}, 
    publisher =	 {IEEE Computer Society Press}
  }