What do Freyd’s Toposes Classify?

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

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