All Melodies are Lost -- Recognizability for weak and strong $α$-ITRMs
For exponentially closed ordinals $\alpha$, we consider recognizability of constructible subsets of $\alpha$ for $\alpha$-(w)ITRMs and their distribution in the constructible hierarchy. In particular, we show that, for class many values of $\alpha$, the sets of $\alpha$-wITRM-computable and $\alpha$-wITRM-recognizable subsets of $\alpha$ are both non-empty, but disjoint, and, also for class many values of $\alpha$, the set of $\alpha$-wITRM-recognizable subsets of $\alpha$ is empty.
PDF AbstractCategories
Logic
