The elementary theory of the recursively enumerable degrees is not \(\aleph _ 0\)-categorical

DOI10.1016/0001-8708(84)90028-8zbMath0559.03027OpenAlexW2091246156MaRDI QIDQ802550

Robert I. Soare, Manuel Lerman, Richard A. Shore

Publication date: 1984

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(84)90028-8

zbMATH Keywords

partially ordered set of r.e. degrees

Mathematics Subject Classification ID

Recursively (computably) enumerable sets and degrees (03D25) Other degrees and reducibilities in computability and recursion theory (03D30) Categoricity and completeness of theories (03C35)

Related Items

The ∀∃-theory of ℛ(≤,∨,∧) is undecidable, Towards characterizing the \(> \omega^2\)-fickle recursively enumerable Turing degrees, Some aspects of effectively constructive mathematics that are relevant to the foundations of neoclassical mathematical economics and the theory of games, Undecidability and 1-types in the recursively enumerable degrees, Annual Meeting of the Association for Symbolic Logic, Berkeley, 1990, Turing computability: structural theory, Model-theoretic properties of Turing degrees in the Ershov difference hierarchy, Lattice embeddings into the recursively enumerable degrees. II, Degree Structures: Local and Global Investigations, The density of the nonbranching degrees, Undecidability and 1-types in intervals of the computably enumerable degrees

Cites Work

• Unnamed Item
• Unnamed Item
• Not every finite lattice is embeddable in the recursively enumerable degrees
• A minimal pair of recursively enumerable degrees
• Lower Bounds for Pairs of Recursively Enumerable Degrees
• Sublattices of the Recursively Enumerable Degrees