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

Jan Šaroch (2020)

Commentationes Mathematicae Universitatis Carolinae

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

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