Definability via Kalimullin pairs in the structure of the enumeration degrees

DOI10.1090/S0002-9947-2014-06157-6zbMath1375.03047OpenAlexW2013208488MaRDI QIDQ5247021

Hristo Ganchev, Mariya Ivanova Soskova

Publication date: 22 April 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2014-06157-6

zbMATH Keywords

first order definabilityenumeration reducibilitytotal enumeration degreesenumeration jumplow enumeration degrees

Mathematics Subject Classification ID

Other degrees and reducibilities in computability and recursion theory (03D30)

Related Items (12)

Elementary theories and structural properties of d-c.e. and n-c.e. degrees ⋮ The automorphism group of the enumeration degrees ⋮ A STRUCTURAL DICHOTOMY IN THE ENUMERATION DEGREES ⋮ The theory of ceers computes true arithmetic ⋮ Unnamed Item ⋮ The enumeration degrees: Local and global structural interactions ⋮ Enumeration Reducibility and Computable Structure Theory ⋮ A Survey of Results on the d-c.e. and n-c.e. Degrees ⋮ Density of the cototal enumeration degrees ⋮ The automorphism group and definability of the jump operator in the \(\omega\)-enumeration degrees ⋮ On Kalimullin pairs ⋮ Defining totality in the enumeration degrees

Cites Work

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• The high/low hierarchy in the local structure of the \(\omega\)-enumeration degrees
• The \(n\)-rea enumeration degrees are dense
• Defining the Turing jump
• A jump inversion theorem for the enumeration jump
• Biinterpretability up to double jump in the degrees below $\mathbf {0}^{\prime }$
• Degree Structures: Local and Global Investigations
• Properly enumeration degrees and the high/low hierarchy
• Weakly semirecursive sets
• Partial degrees and the density problem. Part 2: The enumeration degrees of the Σ₂ sets are dense
• Jumps of quasi-minimal enumeration degrees
• Interpretability and Definability in the Recursively Enumerable Degrees
• Reducibility and Completeness for Sets of Integers
• DEFINABILITY OF THE JUMP OPERATOR IN THE ENUMERATION DEGREES
• On minimal pairs of enumeration degrees
• Interpreting true arithmetic in the local structure of the enumeration degrees
• Cupping and definability in the local structure of the enumeration degrees
• Semirecursive Sets and Positive Reducibility

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