Rethinking the notion of oracle: A link between synthetic descriptive set theory and effective topos theory

02/01/2022

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by   Takayuki Kihara, et al.

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We present three different perspectives of oracle. First, an oracle is a blackbox; second, an oracle is an endofunctor on the category of represented spaces; and third, an oracle is an operation on the object of truth-values. These three perspectives create a link between the three fields, computability theory, synthetic descriptive set theory, and effective topos theory.