THE n-r.e. DEGREES: UNDECIDABILITY AND Σ1 SUBSTRUCTURES-Reference-Cited by-同舟云学术

THE n-r.e. DEGREES: UNDECIDABILITY AND Σ1 SUBSTRUCTURES

Published:2012-06 Issue:01 Volume:12 Page:1250005
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

CAI MINGZHONG¹,SHORE RICHARD A.²,SLAMAN THEODORE A.³

Affiliation:

1. Department of Mathematics, University of Wisconsin, Madison WI 53706, USA

2. Department of Mathematics, Cornell University, Ithaca NY 14853, USA

3. Department of Mathematics, University of California, Berkeley CA 94720, USA

Abstract

We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061312500055

Reference30 articles.

1. Definability and elementary equivalence in the Ershov difference hierarchy

2. On Downey's conjecture

3. The d.r.e. degrees are not dense

Cited by 6 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. Isolation from Side and Cone Avoidance in the 2-Computably Enumerable wtt-Degrees;Journal of Mathematical Sciences;2023-09

2. Turing Computability: Structural Theory;Journal of Mathematical Sciences;2021-05-28

3. Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy;Notre Dame Journal of Formal Logic;2020-11-01

4. Isolation from Side in 2-Computably Enumerable Degrees;Russian Mathematics;2020-08

5. Isolated maximal d.r.e. degrees;Annals of Pure and Applied Logic;2019-04