Some results concerning the SRT 2 2 vs. COH problem | Zendy

Peter Cholak | Zendy; Damir D. Dzhafarov | Zendy; Denis R. Hirschfeldt | Zendy; Ludovic Patey | Zendy

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Some results concerning the SRT 2 2 vs. COH problem

Author(s) -

Peter Cholak,

Damir D. Dzhafarov,

Denis R. Hirschfeldt,

Ludovic Patey

Publication year - 2020

Publication title -

computability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.136

H-Index - 12

eISSN - 2211-3576

pISSN - 2211-3568

DOI - 10.3233/com-190251

Subject(s) - ideal (ethics) , mathematics , point (geometry) , ideal point , mathematical economics , turing , computer science , epistemology , philosophy , geometry , programming language

The SRT2 vs. COH problem is a central problem in computable combinatorics and reverse mathematics, asking whether every Turing ideal that satisfies the principle SRT2 also satisfies the principle COH. This paper is a contribution towards further developing some of the main techniques involved in attacking this problem. We study several principles related to each of SRT2 and COH, and prove results that highlight the limits of our current understanding, but also point to new directions ripe for further exploration.

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