The jump operator on the \(\omega \)-enumeration degrees

DOI10.1016/j.apal.2009.01.003zbMath1183.03031OpenAlexW2023232607MaRDI QIDQ1032630

Ivan N. Soskov, Hristo Ganchev

Publication date: 26 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.apal.2009.01.003

zbMATH Keywords

automorphisms\(\omega \)-enumeration degreesjump operatorhigh and low hierarchies

Mathematics Subject Classification ID

Recursively (computably) enumerable sets and degrees (03D25) Other degrees and reducibilities in computability and recursion theory (03D30)

Related Items

The automorphism group of the enumeration degrees, Unnamed Item, Unnamed Item, Enumeration Reducibility and Computable Structure Theory, The \(\omega\)-Turing degrees, The automorphism group and definability of the jump operator in the \(\omega\)-enumeration degrees, Definability in the Local Theory of the ω-Enumeration Degrees, Defining totality in the enumeration degrees, The high/low hierarchy in the local structure of the \(\omega\)-enumeration degrees

Cites Work

• The \(n\)-rea enumeration degrees are dense
• On automorphisms of the degrees that preserve jumps
• A jump inversion theorem for the enumeration jump
• Uniform regular enumerations
• How enumeration reductibility yields extended Harrington non-splitting
• Partial degrees and the density problem. Part 2: The enumeration degrees of the Σ₂ sets are dense
• Jumps of quasi-minimal enumeration degrees
• DEFINABILITY OF THE JUMP OPERATOR IN THE ENUMERATION DEGREES
• The  -Enumeration Degrees
• Arithmetical Reducibilities I
• Unnamed Item
• Unnamed Item