In Fuchs' Infinite Abelian Groups, it is proved that there exist indecomposable torsion-free abelian groups of every rank smaller than the first strongly inaccessible cardinal. It is natural to ask: is it known for which ranks $\geq$ first strongly inaccessible cardinal there exist such groups?
$\begingroup$
$\endgroup$
asked Aug 18, 2022 at 17:19
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
According to Theorem 2.1 of the following paper, there are indecomposable torsion-free abelian groups of any infinite cardinality.
Shelah, Saharon, Infinite Abelian groups, Whitehead problem and some constructions, Isr. J. Math. 18, 243-256 (1974). ZBL0318.02053. On Shelah's website at https://shelah.logic.at/files/95858/44.pdf
