Embedding and coding below a 1-generic degree

DOI10.1305/NDJFL/1091122498zbMath1066.03045OpenAlexW2171427126MaRDI QIDQ558421

Antonio Montalbán, Noam Greenberg

Publication date: 6 July 2005

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1305/ndjfl/1091122498

zbMATH Keywords

lattice embeddingelementary theorygeneric degree

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Other degrees and reducibilities in computability and recursion theory (03D30) Other Turing degree structures (03D28)

Related Items (4)

THE TURING DEGREES BELOW GENERICS AND RANDOMS ⋮ The theory of the \(\alpha \) degrees is undecidable ⋮ The finite intersection principle and genericity ⋮ Biinterpretability up to double jump in the degrees below $\mathbf {0}^{\prime }$

Cites Work

• Minimal degrees recursive in 1-generic degrees
• Set theory. An introduction to independence proofs. 2nd print
• Definability in the Turing degrees
• First-order theory of the degrees of recursive unsolvability
• Definability in the enumeration degrees
• A 1-generic degree which bounds a minimal degree
• The undecidability of the recursively enumerable degrees
• Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers
• The degrees below a 1-generic degree < 0′
• Interpretability and Definability in the Recursively Enumerable Degrees
• The Theory of the Degrees below 0 ′
• Reducibility orderings: Theories, definability and automorphisms
• Finitely Generated Codings and the Degrees R.E. in a Degree d
• A 1-generic degree with a strong minimal cover
• Distributive Initial Segments of the Degrees of Unsolvability
• On the representation of lattices
• Lattices, equivalence relations, and subgroups
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