Toshiyasu Arai

most citedIterating the recursively Mahlo operations

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math.LO2010

Proof theory for theories of ordinals III: $Π_{N}$ -reflection

Toshiyasu Arai

This paper deals with a proof theory for a theory of $Π_{N}$ -reflecting ordinals using a system of ordinal diagrams. This is a sequel to the previous one(APAL 129)in which a theory…

math.LO2010★ 9 cited

Iterating the recursively Mahlo operations

Toshiyasu Arai

In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo oper…

Proof theory for theories of ordinals III: ΠN​-reflection

Iterating the recursively Mahlo operations

Proof theory for theories of ordinals III: $Π_{N}$ -reflection