The affinity of set theory and abelian group theory.

DOI10.1216/rmjm/1181070012zbMath1043.03001OpenAlexW2008495079MaRDI QIDQ1414984

Paul C. Eklof

Publication date: 3 December 2003

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol32-4/CONT32-4/CONT32-4.html

zbMATH Keywords

surveymeasurable cardinalreflexivityMartin's axiomproper forcing axiomweakly compact cardinalp-groupblack boxaxiom of constructibilityindecomposable groupsingular compactnessButler groupslendernessalmost free groupWhitehead's problem

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Consistency and independence results (03E35) Applications of set theory (03E75) Torsion-free groups, infinite rank (20K20) Other combinatorial set theory (03E05) Abelian groups (20K99) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (1)

Remarks about the history of Abelian groups in England and Germany.

Cites Work

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• On socles of Abelian p-groups in L
• A Boolean power and a direct product of Abelian groups
• On a Boolean power of a torsion free Abelian group
• Assessing continuous bivariate effects among different groups through nonparametric regression models: an application to breast cancer detection
• Crawley's problem on the unique \(\omega\)-elongation of p-groups is undecidable
• \(\omega\)-elongations and Crawley's problem. The solution to Crawley's problem
• On reconstructing separable reduced p-groups with a given socle
• On strongly-non-reflexive groups
• Baer modules over valuation domains
• Martin's axiom implies the existence of certain slender groups
• The consistency of \(\mathrm{Ext}\,(G,\mathbb{Z})=\mathbb{Q}\)
• Whitehead groups may not be free even assuming CH. II
• On endomorphism rings of primary Abelian groups
• Fast freie Abelsche Gruppen mit Endomorphismenring Z
• On Shelah's Whitehead groups and CH
• On endo-rigid, strongly \(\aleph_1\)-free Abelian groups in \(\aleph_1\).
• Every cotorsion-free algebra is an endomorphism algebra
• On iterated torsion products of Abelian \(p\)-groups
• Infinite Abelian groups, Whitehead problem and some constructions
• Singular cohomology in \(L\)
• The structure of Ext\((A,\mathbb{Z})\) and \(V=L\)
• A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals
• Whitehead groups may be not free, even assuming CH. I
• On constructing indecomposable groups in L
• Classification theory and the number of non-isomorphic models
• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
• On uncountable Abelian groups
• Butler groups of arbitrary cardinality
• Valuated vector spaces, Kurepa's hypothesis and Abelian \(p\)-groups
• Cardinal characteristics and the product of countably many infinite cyclic groups
• Incompactness in regular cardinals
• A combinatorial principle and endomorphism rings. I: On \(p\)-groups
• Approximations and endomorphism algebras of modules.
• Endomorphism algebras of large modules with distinguished submodules
• Baer Modules over Domains
• The Functor Bext under the Negation of CH
• On the Existence of κ-Free Abelian Groups
• On Direct Sums of Free Cycles
• The existence of indecomposable abelian groups of arbitrary power
• Uniformization principles
• Butler Groups of Infinite Rank II
• The Structure of ω 1 -Separable Groups
• On the structure of Ext(A,Z) in ZFC⁺
• Whitehead Modules over Domains
• Consistency results about filters and the number of inequivalent growth types
• On the Realizability of Singular Cohomology Groups
• New Criteria for Freeness in Abelian Groups. II
• Whitehead's Problem is Undecidable
• Homological Algebra and Set Theory
• How to Construct Almost Free Groups
• An Application of Set Theory to the Torsion Product of Abelian Groups
• A Homological Characterization of Abelian B 2 -Groups
• When Does Almost Free Imply Free? (For Groups, Transversals, etc.)
• Set Theory Generated by Abelian Group Theory
• A very weak square principle
• Every Cotorsion-Free Ring is an Endomorphism Ring
• It is consistent with ZFC that B1 -groups are not B2
• χ_n-FREE ABELIAN GROUPS
• Maximal abelian subalgebras of real and complex symplectic Lie algebras
• Prescribing Endomorphism Algebras, a Unified Treatment
• On the Decomposition of Groups
• On the freeness of abelian groups: A generalization of Pontryagin's theorem

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