Wellfoundedness proof with the maximal distinguished set

2022/11/16 by Toshiyasu Arai, Arai, Toshiyasu
Computer Science · Mathematics · #03F99 #Benford’s Law and Fraud Detection #Complexity and Algorithms in Graphs #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2211.08619

openalex publication_date 2022/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In arXiv:2208.12944 it is shown that an ordinal sup_N<ωψ_Ω₁(ε_Ω_\mathbbS+N+1) is an upper bound for the proof-theoretic ordinal of a set theory \sf KPℓ^r+(M\prec_Σ₁V). In this paper we show that a second order arithmetic Σ^1-₂-CA+Π¹₁-CA₀ proves the wellfoundedness up to ψ_Ω₁(ε_Ω_\mathbbS+N+1) for each N. It is easy to interpret Σ^1-₂-CA+Π¹₁-CA₀ in \sf KPℓ^r+(M\prec_Σ₁V).

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