Well-foundedness proof for Π¹₁-reflection

2023/04/07 by Toshiyasu Arai, Arai, Toshiyasu
Computer Science · Mathematics · #03F99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2304.03851

openalex publication_date 2023/04/07 · openalex created_date 2023/04/12 · openalex updated_date 2026/07/28

Abstract

In the lecture notes it is shown that an ordinal ψ_Ω(ε_\mathbbS⁺+1) is an upper bound for the proof-theoretic ordinal of a set theory \sf KPω+(M\prec_Σ₁V). In this note we show that \sf KPω+(M\prec_Σ₁V) proves the well-foundedness up to ψ_Ω(ω_n(\mathbbS⁺+1)) for each n.

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