On homogeneity and definability in the first-order theory of the Turing degrees

DOI10.2307/2273376zbMath0521.03027OpenAlexW1981509588MaRDI QIDQ3671144

Richard A. Shore

Publication date: 1982

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

Full work available at URL: https://doi.org/10.2307/2273376

zbMATH Keywords

Turing degreeshomogeneity conjectureelementary equivalent

Mathematics Subject Classification ID

Recursively (computably) enumerable sets and degrees (03D25)

Related Items

Interpolating \(d\)-r.e. and REA degrees between r.e. degrees, The jump is definable in the structure of the degrees of unsolvability, A General Framework for Priority Arguments, The arithmetic and Turing degrees are not elementarily equivalent, The existential theory of the poset of R.E. degrees with a predicate for single jump reducibility, A Rigid Cone in the Truth-Table Degrees with Jump, Bad oracles in higher computability and randomness, The Role of True Finiteness in the Admissible Recursively Enumerable Degrees, Definable degrees and automorphisms of 𝒟, THE THEORY OF THE METARECURSIVELY ENUMERABLE DEGREES, Degree Structures: Local and Global Investigations, Definability in the Recursively Enumerable Degrees, Forcing and reductibilities. II. Forcing in fragments of analysis, Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers

Cites Work

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• First-order theory of the degrees of recursive unsolvability
• Fixed points of jump preserving automorphisms of degrees
• Reducibility orderings: Theories, definability and automorphisms
• A degree-theoretic definition of the ramified analytical hierarchy
• The homogeneity conjecture