### Abstract

Let S be a Scott set, or even an ω-model of WWKL. Then for each A ∈ S, either there is X ∈ S that is weakly 2-random relative to A, or there is X ∈ S that is 1-generic relative to A. It follows that if A_{1},⋯, A_{n} ∈ S are noncomputable, there is X ∈ S such that each A_{i} is Turing incomparable with X, answering a question of Kučera and Slaman.More generally, any ∀∃ sentence in the language of partial orders that holds inD also holds in D^{S}, where D^{S} is the partial order of Turing degrees of elements of S.

Original language | English (US) |
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Pages (from-to) | 392-394 |

Number of pages | 3 |

Journal | Journal of Symbolic Logic |

Volume | 83 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Philosophy
- Logic