Makkai's lost proof of projectivity of N in the free topos
Abstract
We give a categorical proof of the projectivity of N in the free topos -- in proof-theoretic terms, the rule of countable choice for intuitionistic higher-order logic -- based on the unpublished proof of Michael Makkai (c.1980). The presentation aims to be self-contained and accessible to any reader acquainted with elementary toposes and their logic.
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