Ramsey's theorem and cone avoidance

Author:

Dzhafarov Damir D.,Jockusch Carl G.

Abstract

AbstractIt was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low2 homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition CrH, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable 2-coloring of pairs admits a pair of low2 infinite homogeneous sets whose degrees form a minimal pair.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference12 articles.

1. A cohesive set which is not high

2. An alternative, priority-free, solution to Post's problem

3. Π10 classes and degrees of theories;Jockusch;Transactions of the American Mathematical Society,1972

4. Degrees of Unsolvability: A Survey of Results

5. On the strength of Ramsey's theorem;Seetapun;Notre Dame Journal of Formal Logic,1995

Cited by 28 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. Milliken’s Tree Theorem and Its Applications: A Computability-Theoretic Perspective;Memoirs of the American Mathematical Society;2024-01

2. The coding power of a product of partitions;Israel Journal of Mathematics;2023-03-13

3. PARTITION GENERICITY AND PIGEONHOLE BASIS THEOREMS;The Journal of Symbolic Logic;2022-10-03

4. The weakness of the pigeonhole principle under hyperarithmetical reductions;Journal of Mathematical Logic;2020-11-28

5. RAMSEY-LIKE THEOREMS AND MODULI OF COMPUTATION;The Journal of Symbolic Logic;2020-10-27

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3