Limits on jump inversion for strong reducibilities

Author:

Csima Barbara F.,Downey Rod,Ng Keng Meng

Abstract

AbstractWe show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a δ20 set B >tt ∅′ such that there is no c.e. set A with A′ ≡wttB. We also show that there is a Σ20 set C >tt ∅′ such that there is no δ20 set D with D′ ≡wttC.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Lowness properties for strong reducibilities and the computational power of maximal sets;Computability;2023-10-02

2. Effective Domination and the Bounded Jump;Notre Dame Journal of Formal Logic;2020-05-01

3. Bounded-low sets and the high/low hierarchy;Archive for Mathematical Logic;2020-03-27

4. Bounded low and high sets;Archive for Mathematical Logic;2017-04-28

5. A Bounded Jump for the Bounded Turing Degrees;Notre Dame Journal of Formal Logic;2014-01-01

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