Takeuti conjecture

In mathematics, Takeuti's conjecture is the conjecture of Gaisi Takeuti that a sequent formalisation of second-order logic has cut-elimination (Takeuti 1953). It was settled positively:

Takeuti's conjecture is equivalent to the consistency of second-order arithmetic in the sense that each of the statements can be derived from each other in the weak system PRA of arithmetic; consistency refers here to the truth of the Gödel sentence for second-order arithmetic. It is also equivalent to the strong normalization of the Girard/Reynold's System F.

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