Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2009.10582 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- We consider recognizability for Infinite Time Blum-Shub-Smale machines, a model of infinitary computability introduced in Koepke and Seyfferth [KS]. In particular, we show that the lost melody theorem (originally proved for ITTMs in Hamkins and Lewis [HL]), i.e. the existence of non-computable, but recognizable real numbers, holds for ITBMs, that ITBM-recognizable real numbers are hyperarithmetic and that both ITBM-recognizable and ITBM-unrecognizable real numbers appear at every level of the constructible hierarchy below $L_{ω_{1}^{\text{CK}}}$ at which new real numbers appear at all.