Elementary axioms for categories of classes

Alex Simpson

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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
Original languageEnglish
Title of host publicationLogic in Computer Science, 1999. Proceedings. 14th Symposium on
Number of pages9
Publication statusPublished - 1999


  • category theory
  • formal languages
  • set theory
  • axiomatization
  • axioms
  • categories of classes
  • classic structure
  • elementary axioms
  • intuitionistic Zermelo-Fraenkel set theory
  • regular category
  • topos
  • Buildings
  • Computer science
  • Electrical capacitance tomography
  • Equations
  • Geometry
  • Informatics
  • Logic
  • Mathematics
  • Pulleys
  • Set theory


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