Classes of Ulm type and coding rank-homogeneous trees in other structures

DOI10.2178/JSL/1309952523zbMath1241.03042OpenAlexW2160413100MaRDI QIDQ3173529

Alexander G. Melnikov, Ekaterina B. Fokina, S. Quinn, C. Safranski, Julia F. Knight

Publication date: 10 October 2011

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

Full work available at URL: https://doi.org/10.2178/jsl/1309952523

zbMATH Keywords

Boolean algebrasabelian \(p\)-groupsTuring-computable embeddingabelian torsion groupsclass of Ulm typerank-homogeneous trees

Mathematics Subject Classification ID

Trees (05C05) Applications of logic to group theory (20A15) Finite nilpotent groups, (p)-groups (20D15) Structure theory of Boolean algebras (06E05) Torsion groups, primary groups and generalized primary groups (20K10) Computable structure theory, computable model theory (03C57) Model theory of denumerable and separable structures (03C15)

Related Items (9)

Comparing classes of finite sums ⋮ Torsion-free abelian groups with optimal Scott families ⋮ ASSIGNING AN ISOMORPHISM TYPE TO A HYPERDEGREE ⋮ Isomorphism relations on computable structures ⋮ Turing computable embeddings, computable infinitary equivalence, and linear orders ⋮ COMPUTABLE ABELIAN GROUPS ⋮ Computable embeddings for pairs of linear orders ⋮ Computable topological abelian groups ⋮ On \(\Delta_2^0\)-categoricity of equivalence relations

Cites Work

• The isomorphism problem for torsion-free abelian groups is analytic complete
• Computable structures and the hyperarithmetical hierarchy
• Degree spectra and computable dimensions in algebraic structures
• Undecidable fragments of elementary theories
• On the Complexity of the Classification Problem for Torsion-Free Abelian Groups of Finite Rank
• A Borel reductibility theory for classes of countable structures
• THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO
• Scott sentences and admissible sets
• Models with compactness properties relative to an admissible language
• Model Theory
• The isomorphism relation on countable torsion free abelian groups
• The effective Borel hierarchy
• Complexity of Categorical Theories with Computable Models

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