Finding bases of uncountable free abelian groups is usually difficult

DOI10.1090/tran/7232zbMath1414.03006arXiv1709.02326OpenAlexW2963957935MaRDI QIDQ4608785

Noam Greenberg, Dan Turetsky, Linda Brown Westrick

Publication date: 28 March 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02326

zbMATH Keywords

definabilityfree abelian groupcomputable algebraadmissible computability

Mathematics Subject Classification ID

Computable structure theory, computable model theory (03C57) Theory of numerations, effectively presented structures (03D45) Abelian groups (20K99) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Related Items

UNIFORM PROCEDURES IN UNCOUNTABLE STRUCTURES, ON THE COMPLEXITY OF CLASSIFYING LEBESGUE SPACES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shelah's singular compactness theorem.
• Negative solutions to Post's problem. II
• Recursion theory week. Proceedings of a conference held in Oberwolfach, Germany, March 19-25, 1989
• Infinite Abelian groups, Whitehead problem and some constructions
• A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals
• The theory of topological commutative groups
• Effectively categorical abelian groups
• On the Existence of κ-Free Abelian Groups
• Effective procedures in field theory
• The unsolvability of the problem of the equivalence of words in a group and several other problems in algebra
• THE WORD PROBLEM
• Subgroups of finitely presented groups
• Ordinal Computability
• Adding a closed unbounded set
• Recursively enumerable vector spaces
• UNIFORM PROCEDURES IN UNCOUNTABLE STRUCTURES
• Effective Mathematics of the Uncountable
• New Criteria for Freeness in Abelian Groups
• COMPUTABILITY AND UNCOUNTABLE LINEAR ORDERS I: COMPUTABLE CATEGORICITY
• COMPUTABILITY AND UNCOUNTABLE LINEAR ORDERS II: DEGREE SPECTRA
• CONSTRUCTIVE ALGEBRAS I
• Classes of structures with universe a subset of  1
• The Arithmetical Hierarchy in the Setting of $\omega_1$
• The role of true finiteness in the admissible recursively enumerable degrees
• Computable Algebra, General Theory and Theory of Computable Fields
• The fine structure of the constructible hierarchy