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# Optimal results on ITRM-recognizability

Type of Publication: | Preprint |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-255802 |

Author: | Carl, Merlin |

Year of publication: | 2013 |

ArXiv-ID: | arXiv:1306.5128 |

Summary: |
Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in Gödels constructible universe L.
In particular, we show that new unrecognizables are generated at every index $\gamma\geq\omega_{\omega}^{CK}$. We give a machine-independent characterization of recognizability by proving that a real $r$ is recognizable iff it is $\Sigma_{1}$-definable over $L_{\omega_{\omega}^{CK,r}}$ and that $r\in L_{\omega_{\omega}^{CK,r}}$ for every recognizable real $r$ and show that either every or no $r$ with $r\in L_{\omega_{\omega}^{CK,r}}$ generated over an index stage $L_{\gamma}$ is recognizable. Finally, the techniques developed along the way allow us to prove that the halting number for $ITRM$s is recognizable and that the set of $ITRM$-computable reals is not $ITRM$-decidable. |

Subject (DDC): | 510 Mathematics |

Link to License: | In Copyright |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:dee3ea702bf082834d04a46108326284

CARL, Merlin, 2013. Optimal results on ITRM-recognizability

@unpublished{Carl2013Optim-25580, title={Optimal results on ITRM-recognizability}, year={2013}, author={Carl, Merlin} }

Carl_255802.pdf | 140 |