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Takeuti's 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:
* By Tait, using a semantic technique for proving cut-elimination, based on work by Schütte (Tait 1966);
* Independently by Takahashi by a similar technique (Takahashi 1967);
* It is a corollary of Jean-Yves Girard's syntactic proof of strong normalization for System F.
Takeuti's conjecture is equivalent to the consistency of second-order arithmetic and to the strong normalization of the Girard/Reynold's System F.
==See also==
* Hilbert's second problem
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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