Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers

DOI10.2307/2274273zbMath0574.03026OpenAlexW2083623332MaRDI QIDQ3691653

Carl G. jun. Jockusch, Richard A. Shore

Publication date: 1984

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2274273

zbMATH Keywords

arithmetic degreeshomogeneity problem

Mathematics Subject Classification ID

Other degrees and reducibilities in computability and recursion theory (03D30) Hierarchies of computability and definability (03D55)

Related Items

Lowness for genericity ⋮ Nullifying randomness and genericity using symmetric difference ⋮ Elementary theories and structural properties of d-c.e. and n-c.e. degrees ⋮ Members of countable \(\Pi ^ 0_ 1\) classes ⋮ Iterated relative recursive enumerability ⋮ On the problem of the critical bound ⋮ Working below a high recursively enumerable degree ⋮ THE n-r.e. DEGREES: UNDECIDABILITY AND Σ₁ SUBSTRUCTURES ⋮ Extending properly n - REA sets1 ⋮ HTP-COMPLETE RINGS OF RATIONAL NUMBERS ⋮ A non-inversion theorem for the jump operator ⋮ Bounded low and high sets ⋮ Ershov hierarchy and the T-jump ⋮ Interpolating \(d\)-r.e. and REA degrees between r.e. degrees ⋮ Strong jump-traceability. II: \(K\)-triviality ⋮ STRONG JUMP-TRACEABILITY ⋮ 2-minimality, jump classes and a note on natural definability ⋮ The jump is definable in the structure of the degrees of unsolvability ⋮ Continuous randomness via transformations of 2-random sequences ⋮ Turing reducibility in the fine hierarchy ⋮ Reals n-generic relative to some perfect tree ⋮ On the main scientific achievements of Victor Selivanov ⋮ DIRECT AND LOCAL DEFINITIONS OF THE TURING JUMP ⋮ Simple structures with complex symmetry ⋮ A bounded jump for the bounded Turing degrees ⋮ \textit{CEA} operators and the ershov hierarchy ⋮ A splitting theorem for $n-REA$ degrees ⋮ Turing degrees in refinements of the arithmetical hierarchy ⋮ The \(n\)-rea enumeration degrees are dense ⋮ Local Definitions in Degree Structures: The Turing Jump, Hyperdegrees and Beyond ⋮ Isolation in the CEA hierarchy ⋮ Embedding and coding below a 1-generic degree ⋮ Turing computability: structural theory ⋮ Precomplete numberings ⋮ Measure-theoretic applications of higher Demuth’s Theorem ⋮ Initial segments of the degrees of size \(\aleph _ 1\) ⋮ Decomposing Borel functions using the Shore–Slaman join theorem ⋮ Mass problems associated with effectively closed sets ⋮ Degree Structures: Local and Global Investigations ⋮ Completing pseudojump operators ⋮ Jumps of certain classes of \(\Delta_ 2^ 0\)-sets ⋮ Splitting theorems in recursion theory

Cites Work

• Unnamed Item
• Countable admissible ordinals and hyperdegrees
• First-order theory of the degrees of recursive unsolvability
• Countable retracing functions and \(\Pi_2^0\) predicates
• On the degrees less than 0'
• The upper semi-lattice of degrees of recursive unsolvability
• Degrees joining to 0′
• On homogeneity and definability in the first-order theory of the Turing degrees
• Jumping through the transfinite: the master code hierarchy of Turing degrees
• Definable degrees and automorphisms of 𝒟
• Reducibility orderings: Theories, definability and automorphisms
• A degree-theoretic definition of the ramified analytical hierarchy
• Transfinite extensions of Friedberg's completeness criterion
• The homogeneity conjecture
• Some applications of forcing to hierarchy problems in arithmetic
• Some contrasts between degrees and the arithmetical hierarchy