A computable ℵ0-categorical structure whose theory computes true arithmetic

DOI10.2178/JSL/1268917501zbMath1201.03020OpenAlexW2121539673MaRDI QIDQ3570169

Antonio Montalbán, Bakhadyr Khoussainov

Publication date: 24 June 2010

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

Full work available at URL: https://doi.org/10.2178/jsl/1268917501

zbMATH Keywords

arithmetical complexitycomputable structurecountably categorical structure

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Computable structure theory, computable model theory (03C57) Theory of numerations, effectively presented structures (03D45) Categoricity and completeness of theories (03C35)

Related Items (6)

ASSIGNING AN ISOMORPHISM TYPE TO A HYPERDEGREE ⋮ Enumeration Reducibility and Computable Structure Theory ⋮ CODING IN GRAPHS AND LINEAR ORDERINGS ⋮ Constructing decidable graphs from decidable structures ⋮ The degrees of categorical theories with recursive models ⋮ Computing and dominating the Ryll-Nardzewski function

Cites Work

• Decidable models
• Computable models of theories with few models
• Computable structures and the hyperarithmetical hierarchy
• Foundations of recursive model theory
• Vaught's theorem recursively revisited
• Nonarithmetical ℵ₀-categorical theories with recursive models
• Trivial, strongly minimal theories are model complete after naming constants
• On the computability-theoretic complexity of trivial, strongly minimal models

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