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arXiv · 2304.03851

Well-foundedness proof for $\Pi^{1}_{1}$-reflection

Toshiyasu Arai
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Abstract

In the lecture notes it is shown that an ordinal $\psi_{\Omega}(\varepsilon_{\mathbb{S}^{+}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$. In this note we show that ${\sf KP}\omega+(M\prec_{\Sigma_{1}}V)$ proves the well-foundedness up to $\psi_{\Omega}(\omega_{n}(\mathbb{S}^{+}+1))$ for each $n$.

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Toshiyasu Arai. 2023-04-07. Well-foundedness proof for $\Pi^{1}_{1}$-reflection. https://arxiv.org/abs/2304.03851

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