论文标题
具有最大杰出集合的良好状态证明
Wellfoundedness proof with the maximal distinguished set
论文作者
论文摘要
在Arxiv：2208.12944中，显示出一个顺序的$ \ sup_ {n <ω}ψ_{ω_{ω_{1}}}（\ varepsilon_ {\ varepsilon_ {ω_{\ mathbb {s} kp} \ ell^{r}+（m \ prec_ {σ_{1}} v）$。在本文中，我们表明二阶算术算术$σ^{1 - } _ {2} \ mbox {-ca}+π^{1} _ {1} \ mbox {-ca} _ {0} $ψ_{ω_{1}}（\ varepsilon_ {ω_ {\ mathbb {s}+n+1}}}）$。很容易解释$σ^{1-} _ {2} \ mbox {-ca}+π^{1} _ {1} \ mbox {-ca} _ {0} $ in $ {\ sf kp}
In arXiv:2208.12944 it is shown that an ordinal $\sup_{N<ω}ψ_{Ω_{1}}(\varepsilon_{Ω_{\mathbb{S}+N}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\ell^{r}+(M\prec_{Σ_{1}}V)$. In this paper we show that a second order arithmetic $Σ^{1-}_{2}\mbox{-CA}+Π^{1}_{1}\mbox{-CA}_{0}$ proves the wellfoundedness up to $ψ_{Ω_{1}}(\varepsilon_{Ω_{\mathbb{S}+N+1}})$ for each $N$. It is easy to interpret $Σ^{1-}_{2}\mbox{-CA}+Π^{1}_{1}\mbox{-CA}_{0}$ in ${\sf KP}\ell^{r}+(M\prec_{Σ_{1}}V)$.
