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created stub for Barr’s theorem (If a statement in geometric logic is deducible from a geometric theory using classical logic and the axiom of choice, then it is also deducible from it in constructive mathematics.)
Former wording claimed that the construction of the Barr cover of a topos is “highly non-constructive”, which is false. Rather, the Barr cover is a Boolean localic topos without further conditions, and the non-constructive part is showing that this is sufficient for the axiom of choice to hold in the covering topos.
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