On the nontrivial solvability of systems of homogeneous linear equations over Z in ZFC

Abstract

Motivated by the paper by H. Herrlich, E.

Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals kappa, an arbitrary nonempty system S of homogeneous Z-linear equations is nontrivially solvable in Z provided that each of its subsystems of cardinality less than kappa is nontrivially solvable in Z?

Keywords

• homogeneous Z-linear equation
• kappa-free group
• L-omega 1 omega-compact cardinal