THE THEORY OF THE METARECURSIVELY ENUMERABLE DEGREES

DOI10.1142/S0219061306000505zbMath1109.03040MaRDI QIDQ5485749

Theodore A. Slaman, Richard A. Shore, Noam Greenberg

Publication date: 4 September 2006

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

zbMATH Keywords

elementary equivalenceadmissible recursionmetarecursion theorymetarecursively enumerable degreesSlaman-Woodin sets

Mathematics Subject Classification ID

Recursively (computably) enumerable sets and degrees (03D25) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Related Items (1)

The theory of the \(\alpha \) degrees is undecidable

Cites Work

• On the theory of the PTIME degrees of the recursive sets
• On the recursive functions of ordinal numbers
• Techniques of admissible recursion theory
• The irregular and non-hyperregular \(\alpha\)-r.e. degrees
• Conjectures and questions from Gerald Sacks's \textit{Degrees of unsolvability}
• The undecidability of the recursively enumerable degrees
• On homogeneity and definability in the first-order theory of the Turing degrees
• Finite injury and Σ₁-induction
• Interpretability and Definability in the Recursively Enumerable Degrees
• A recursively enumerable degree which will not split over all lesser ones
• The recursively enumerable α-degrees are dense
• The role of true finiteness in the admissible recursively enumerable degrees
• A formalization of the theory of ordinal numbers
• Metarecursively enumerable sets and admissible ordinals
• Metarecursive sets
• Metarecursively enumerable sets and their metadegrees
• Some minimal pairs of α-recursively enumerable degrees
• The constructive second number class
• On notation for ordinal numbers
• Consistency-Proof for the Generalized Continuum-Hypothesis

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