A classification of jump operators

DOI10.2307/2273146zbMath0524.03029OpenAlexW2035687451MaRDI QIDQ3037408

J. R. Steel

Publication date: 1982

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

Full work available at URL: https://doi.org/10.2307/2273146

zbMATH Keywords

Turing reducibilitydeterminacyTuring degreesjump operatorsordinal measure of strength for theories in the language of second order arithmetic

Mathematics Subject Classification ID

Other degrees and reducibilities in computability and recursion theory (03D30) Determinacy principles (03E60)

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A Π¹₁-uniformization principle for reals ⋮ Hod mice and the Mouse Set Conjecture ⋮ The comparison lemma ⋮ Topological reducibilities for discontinuous functions and their structures ⋮ Uniform Martin’s conjecture, locally ⋮ Inner model operators in \(L(\mathbb{R})\) ⋮ A characterization of jump operators ⋮ There is no degree invariant half-jump ⋮ Well-Quasi Orders and Hierarchy Theory ⋮ Realizing an \(\mathrm{AD}^+\) model as a derived model of a premouse ⋮ Degree Spectra of Relations on a Cone ⋮ The uniform Martin’s conjecture for many-one degrees ⋮ Inner Model Operators and the Continuum Hypothesis ⋮ Degree-invariant, analytic equivalence relations without perfectly many classes ⋮ Turing degrees in Polish spaces and decomposability of Borel functions

Cites Work

• Jumping through the transfinite: the master code hierarchy of Turing degrees
• A degree-theoretic definition of the ramified analytical hierarchy
• The axiom of determinateness and reduction principles in the analytical hierarchy
• The fine structure of the constructible hierarchy