{"paper":{"title":"On the nontrivial solvability of systems of homogeneous linear equations over $\\mathbb Z$ in ZFC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jan \\v{S}aroch","submitted_at":"2018-12-17T18:58:08Z","abstract_excerpt":"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 $\\mathbb Z$?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06958","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}