June 2022

There’s a 2009 article by Arai on interated recursive Mahloness. The main idea of the paper is that stronger systems of reflection can be analysed in terms of iterated $\Pi_2$-reflection. In section 5, Arai writes the following: A $\Pi_3$-reflecting ordinal $K$ is understood to be …

I’m back. Surprise! I’m making a simplified collapsing function reaching $\Pi_\omega$-ref. $K$ denotes the least $+1$-stable, First, let’s set up our reflection configurations. We define them by stating that for ordinal $\kappa$, integer $n>0$, ordinal $\alpha$, and reflection configurations $\mathbb{X},\ldots$, $(\kappa,n,\alpha,\mathbb{X},\ldots)$ is a reflection configuration, provided $\kappa$ is $\Pi_{n+1}$-reflecting on $\mathcal A\mathbb X\cap\ldots$. The variables