What do Freyd’s Toposes Classify?

Logica Universalis 7 (3):335-340 (2013)

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
Keywords Axiom of choice  classifying topos  geometric theory  Freyd models  Freydian category
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DOI 10.1007/s11787-013-0085-x
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