Coloring grids

• Autorzy: Ramiro de la Vega
• Języki publikacji: EN

Abstrakty

EN

A structure $𝓐 = (A;E_{i})_{i∈n}$ 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 χ: A → n is an acceptable coloring if for all i ∈ n, the $χ^{-1}(i)$ intersects each $E_{i}$-equivalence class in a finite set. If B is a set, then the n-cube Bⁿ may be seen as an n-grid, where the equivalence classes of $E_{i}$ are the lines parallel to the ith coordinate axis. We use elementary submodels of the universe to characterize those n-grids which admit an acceptable coloring. As an application we show that if an n-grid 𝓐 does not admit an acceptable coloring, then every finite n-cube is embeddable in 𝓐.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E05: Other combinatorial set theory
• 51M05: Euclidean geometries (general) and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 3
• Strony: 283-289

Daty

wydano

2015

Twórcy

autor

Ramiro de la Vega

• Departamento de Matemáticas, Universidad de los Andes, Cra 1 No. 18A-12, Bogotá, Colombia

Identyfikatory

DOI

10.4064/fm228-3-5