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For questions on the formal system in mathematical logic for expressing effective functions, programs and computation, and proofs, using abstract notions of functions and combining them through binding and substitution.
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Easier Girard's paradox in a circular pure type system (PTS)
System U is an inconsistent PTS in that one has a term of type $\bot = \forall p\colon \ast \ldotp p$, and such a term is explicitly constructed in Hurkens' A Simplification of Girard's Paradox.
One- …