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

Jan Šaroch

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 2, page 155-164
  • ISSN: 0010-2628

Abstract

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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 κ , 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 κ is nontrivially solvable in ℤ ?

How to cite

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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 61.2 (2020): 155-164. <http://eudml.org/doc/297296>.

@article{Šaroch2020,
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 $\mathbb \{Z\}$-linear equations is nontrivially solvable in $\mathbb \{Z\}$ provided that each of its subsystems of cardinality less than $\kappa $ is nontrivially solvable in $\mathbb \{Z\}$?},
author = {Šaroch, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {homogeneous $\mathbb \{Z\}$-linear equation; $\kappa $-free group; $\mathcal \{L\}_\{\omega _1\omega \}$-compact cardinal},
language = {eng},
number = {2},
pages = {155-164},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb \{Z\}$ in ZFC},
url = {http://eudml.org/doc/297296},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Šaroch, Jan
TI - On the nontrivial solvability of systems of homogeneous linear equations over $\mathbb {Z}$ in ZFC
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 2
SP - 155
EP - 164
AB - 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 $\mathbb {Z}$?
LA - eng
KW - homogeneous $\mathbb {Z}$-linear equation; $\kappa $-free group; $\mathcal {L}_{\omega _1\omega }$-compact cardinal
UR - http://eudml.org/doc/297296
ER -

References

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