{"paper":{"title":"Coloring Grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ramiro de la Vega","submitted_at":"2014-09-18T14:25:59Z","abstract_excerpt":"A structure $\\mathcal{A}=\\left(A;E_i\\right)_{i\\in n}$ where each $E_i$ is an equivalence relation on $A$ is called an $n$-grid if any two equivalence classes coming from distinct $E_i$'s intersect in a finite set. A function $\\chi: A \\to n$ is an acceptable coloring if for all $i \\in n$, the set $\\chi^{-1}(i)$ intersects each $E_i$-equivalence class in a finite set. If $B$ is a set, then the $n$-cube $B^n$ may be seen as an $n$-grid, where the equivalence classes of $E_i$ are the lines parallel to the $i$-th coordinate axis. We use elementary submodels of the universe to characterize those $n$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5312","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"}