pure intuitionistic type theory

philosophy of mathematics

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In foundations of mathematics: Intuitionistic type theories
…will be the case for pure intuitionistic type theory ℒ₀, in which types, terms, and theorems are all defined inductively. In ℒ₀ there are no types, terms, or theorems other than those that follow from the definition of type theory. ℒ₀ is adequate for the constructive part of the usual…
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