Whitehead groups may be not free, even assuming CH. I

DOI10.1007/BF02759809zbMath0369.02035OpenAlexW2072419054WikidataQ56169125 ScholiaQ56169125MaRDI QIDQ1243716

Saharon Shelah

Publication date: 1977

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02759809

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Consistency and independence results (03E35) Graph theory (05C99) Abelian groups (20K99) Metamathematical considerations in group theory (20A10)

Related Items (37)

On the structure of Ext(A,Z) in ZFC⁺ ⋮ Unnamed Item ⋮ Hereditarily separable groups and monochromatic uniformization ⋮ Some observations on the Baireness of \(C_{k}(X)\) for a locally compact space \(X\) ⋮ Diamonds, uniformization ⋮ Uniformization principles ⋮ On the rank of Ext ⋮ Unnamed Item ⋮ Iterated Souslin forcing, the principles \(\diamondsuit(E)\) and a generalisation of the axiom SAD ⋮ Forcing axioms for λ‐complete μ+$\mu ^+$‐c.c. ⋮ The uniformization property for \(chi_ 2\). ⋮ Negating the Galvin property ⋮ The consistency of \(\mathrm{Ext}\,(G,\mathbb{Z})=\mathbb{Q}\) ⋮ Filtration-equivalent \(\aleph_1\)-separable Abelian groups of cardinality \(\aleph_1\). ⋮ Whitehead groups may not be free even assuming CH. II ⋮ Set Theory Generated by Abelian Group Theory ⋮ The affinity of set theory and abelian group theory. ⋮ Lattices and cohomological Mackey functors for finite cyclic \(p\)-groups ⋮ On the number of ${L}_{\infty \omega _1}$-equivalent non-isomorphic models ⋮ Infinite groups ⋮ Not collapsing cardinals \(\leq\kappa\) in \((<\kappa)\)-support iterations ⋮ On Whitehead modules ⋮ More on weak diamond ⋮ The monadic theory of \((\omega{}_ 2,<)\) may be complicated ⋮ Hedetniemi's conjecture for uncountable graphs ⋮ A non-reflexive Whitehead group ⋮ Diagonal Prikry extensions ⋮ The consistency with CH of some consequences of Martin's axiom plus \(2^{\aleph_0}>\aleph_1\) ⋮ A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\) ⋮ Uniformization and the diversity of Whitehead groups ⋮ On uncountable Abelian groups ⋮ A consistent counterexample in the theory of collectionwise Hausdorff spaces ⋮ On countable von Neumann regular rings ⋮ A model with Suslin trees but no minimal uncountable linear orders other than \(\omega_1\) and \(- \omega_1\) ⋮ Additivity of metrizability and related properties ⋮ Modules ⋮ A guessing principle from a Souslin tree, with applications to topology

Cites Work

• Unnamed Item
• Whitehead groups may not be free even assuming CH. II
• Infinite Abelian groups, Whitehead problem and some constructions
• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
• On uncountable Abelian groups
• The Souslin problem
• Iterated Cohen extensions and Souslin's problem
• Whitehead's Problem is Undecidable
• Internal cohen extensions
• Trees

This page was built for publication: Whitehead groups may be not free, even assuming CH. I