论文信息 - The ordinals of the systems of second order arithmetic with the provably Δ 2 1 -comprehension axiom and with the Δ 2 1 -comprehension axiom respectively

The ordinals of the systems of second order arithmetic with the provably Δ 2 1 -comprehension axiom and with the Δ 2 1 -comprehension axiom respectively

Definition 1.15. A proof of second order arithmetic in the tree form formulation with G L C as its logical basis (see [5] for the precise definition) (Including substitution as one of the rules of inference) is called (3-) reducible if it satisfies the following.

Mariko Yasugi | Gaisi Takeuti | G. Takeuti | M. Yasugi

[1] Gaisi Takeuti,et al. Consistency Proofs of Subsystems of Classical Analysis , 1967 .

[2] Akiko Kino,et al. Formalization of the Theory of Ordinal Diagrams of Infinite Order , 1970 .

[3] Gaisi Takeuti. The Π 1 1 -comprehension schema and ω-rules , 1968 .

[4] G. Takeuti. On the Formal Theory of the Ordinal Diagrams , 1958 .

[5] W. W. Tait. Applications of the Cut Elimination Theorem to Some Subsystems of Classical Analysis , 1970 .