The computable dimension of ordered abelian groups

DOI10.1016/S0001-8708(02)00042-7zbMath1031.03058OpenAlexW1983504991MaRDI QIDQ1873769

Steffen Lempp, Sergei S. Goncharov, D. Reed Solomon

Publication date: 27 May 2003

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

Full work available at URL: https://doi.org/10.1016/s0001-8708(02)00042-7

zbMATH Keywords

ordered groupscomputabilitycomputable model theory

Mathematics Subject Classification ID

Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Computable structure theory, computable model theory (03C57)

Related Items (23)

Computable dimension for ordered fields ⋮ A robuster Scott rank ⋮ Computable valued fields ⋮ Iterated effective embeddings of abelian p-groups ⋮ Computable isomorphisms for certain classes of infinite graphs ⋮ Computable Heyting algebras with distinguished atoms and coatoms ⋮ On Constructive Nilpotent Groups ⋮ Analytic computable structure theory and $L^p$ spaces ⋮ The complexity of computable categoricity ⋮ Independence in computable algebra ⋮ Algebraic structures computable without delay ⋮ Computable isomorphisms of Boolean algebras with operators ⋮ Effective categoricity of equivalence structures ⋮ COMPUTABLE ABELIAN GROUPS ⋮ Categoricity spectra of computable structures ⋮ Computable categoricity of trees of finite height ⋮ Non-density in punctual computability ⋮ Effective categoricity of abelian \(p\)-groups ⋮ Categorical linearly ordered structures ⋮ d-computable categoricity for algebraic fields ⋮ Categoricity properties for computable algebraic fields ⋮ Computable topological abelian groups ⋮ Индексное множество автоустойчивых упорядоченных абелевых групп

Cites Work

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• Some constructivizations of Abelian groups
• Recursion theory and ordered groups
• Autostability of models
• Strong and weak constructivization and computable families
• \(\Pi_{1}^{0}\) classes and orderable groups
• Nilpotent groups of finite algorithmic dimension
• Effective content of field theory
• Recursively Categorical Linear Orderings
• Recursively enumerable sets and degrees
• Computable Algebra, General Theory and Theory of Computable Fields
• Reverse mathematics and fully ordered groups

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