Failure of singular compactness for Hom

Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah

Assuming Gödel's axiom of constructibility $V=L$, we construct a $\ddot{I}‡$-free abelian group $G$ of singular cardinality for some suitable cardinal $\ddot{I}‡$ which is regular and uncountab…