  Following a recent paper by Herrlich and Tachtsis, we investigate in ZFC the
following compactness question: for which unountable cardinals $\kappa$, an
arbitrary nonempty system $S$ of homogeneous $\mathbb Z$-linear equations is
nontrivially solvable in $\mathbb Z$ provided that each its nonempty subsystem
of cardinality $<\kappa$ is nontrivially solvable in $\mathbb Z$?
