Abstract
We describe a method for presenting (a topos closely related to) either of Freyd’s topos-theoretic models for the independence of the axiom of choice as the classifying topos for a geometric theory. As an application, we show that no such topos can admit a geometric morphism from a two-valued topos satisfying countable dependent choice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blass, A.R., Scedrov, A.: Freyd’s Models for the independence of the axiom of choice. Memoirs Am. Math. Soc. 404, (1989)
Fourman M.P.: Sheaf models for set theory. J. Pure Appl. Algebra. 19, 91–101 (1980)
Fourman, M.P., Hyland, J.M.E.: Sheaf models for analysis. In: Applications of Sheaves, Lecture Notes in Mathematics, vol. 753, pp. 280–301. Springer, Berlin (1979)
Freyd P.J.: The axiom of choice. J. Pure Appl. Algebra. 19, 103–125 (1980)
Johnstone, P.T.: Sketches of an Elephant: a Topos Theory Compendium. In: Oxford logic guides, vols. 1–2, pp. 44–45. Oxford University Press, Oxford (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Johnstone, P. What do Freyd’s Toposes Classify?. Log. Univers. 7, 335–340 (2013). https://doi.org/10.1007/s11787-013-0085-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11787-013-0085-x