论文标题
无限时间blum-shub-smale机器的丢失旋律定理
The Lost Melody Theorem for Infinite Time Blum-Shub-Smale Machines
论文作者
论文摘要
我们考虑了无限时间blum-shub-smale机器的可识别性，这是一种在Koepke和Seyfferth [KS]中引入的无限计算性模型。 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}}}} $完全出现新的实数。
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.
