Abstract
This paper deals with a proof theory for a theory T N of \(\Pi _{N}\)-reflecting ordinals using a system \(\mathit{Od}(\Pi _{N})\) of ordinal diagrams. This is a sequel to the previous one (Arai, Ann Pure Appl Log 129:39–92, 2004) in which a theory for \(\Pi _{3}\)-reflecting ordinals is analysed proof-theoretically.
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Notes
- 1.
For simplicity we suppress the parameter. Correctly \(\forall u(A(u)\, \rightarrow \,\exists z(u < z\,\&\,A^{z}(u)))\).
References
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Arai, T. (2015). Proof Theory for Theories of Ordinals III: \(\Pi _{N}\) -Reflection. In: Kahle, R., Rathjen, M. (eds) Gentzen's Centenary. Springer, Cham. https://doi.org/10.1007/978-3-319-10103-3_14
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DOI: https://doi.org/10.1007/978-3-319-10103-3_14
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