The degree of a \(\Sigma_ n\) cut

DOI10.1016/0168-0072(90)90021-SzbMath0713.03028OpenAlexW2055041806MaRDI QIDQ749530

D. Kharzeev

Publication date: 1990

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(90)90021-s

zbMATH Keywords

minimal pairsminimal degreesreverse recursion theory

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Recursively (computably) enumerable sets and degrees (03D25)

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Fragments of Kripke-Platek set theory and the metamathematics of \(\alpha \)-recursion theory ⋮ \(\Sigma_ 2\) induction and infinite injury priority arguments. II. Tame \(\Sigma_ 2\) coding and the jump operator ⋮ HOW STRONG IS RAMSEY’S THEOREM IF INFINITY CAN BE WEAK? ⋮ \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs ⋮ 1-Generic Degrees Bounding Minimal Degrees Revisited ⋮ \(\Delta_{2}\) degrees without \(\Sigma_{1}\) induction ⋮ Weaker cousins of Ramsey's theorem over a weak base theory ⋮ The inductive strength of Ramsey's theorem for pairs ⋮ The minimal e-degree problem in fragments of Peano arithmetic ⋮ Σ₂ Induction and infinite injury priority argument, Part I: Maximal sets and the jump operator ⋮ In search of the first-order part of Ramsey's theorem for pairs

Cites Work

• Hyperhypersimple sets and \(\Delta _ 2\) systems
• A note on the Mac Dowell-Specker theorem
• Σ₂-collection and the infinite injury priority method
• Finite injury and Σ₁-induction
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