Geodesic
On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb Z$ in ZFC
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 155-164.

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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 $\mathbb Z$-linear equations is nontrivially solvable in $\mathbb Z$ provided that each of its subsystems of cardinality less than $\kappa$ is nontrivially solvable in $\mathbb Z$?
DOI : 10.14712/1213-7243.2020.017
Classification : 03E35, 03E55, 08A45, 13C10, 20K30
Keywords: homogeneous $\mathbb Z$-linear equation; $\kappa$-free group; $\mathcal L_{\omega_1\omega}$-compact cardinal 
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     title = {On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb Z$ in {ZFC}},
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Šaroch, Jan. On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb Z$ in ZFC. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 155-164. doi : 10.14712/1213-7243.2020.017. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.017/

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