Infinite Monochromatic Sumsets for Colourings of the Reals
| Autor: | Dániel T. Soukup, Imre Leader, Saharon Shelah, Paul A. Russell, Péter Komjáth, Zoltán Vidnyánszky |
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| Přispěvatelé: | Apollo - University of Cambridge Repository |
| Rok vydání: | 2019 |
| Předmět: |
03E02
03E35 05D10 Pure mathematics partition relation Applied Mathematics General Mathematics 010102 general mathematics Sumset Mathematics - Logic 0102 computer and information sciences continuum 01 natural sciences colouring 010201 computation theory & mathematics Consistency (statistics) FOS: Mathematics monochromatic Mathematics - Combinatorics Combinatorics (math.CO) Continuum (set theory) Monochromatic color 0101 mathematics Logic (math.LO) Constant (mathematics) Mathematics |
| DOI: | 10.17863/cam.35944 |
| Popis: | N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of $\mathbb R$ so that no infinite sumset $X+X=\{x+y:x,y\in X\}$ is monochromatic. Our aim in this paper is to prove a consistency result in the opposite direction: we show that, under certain set-theoretic assumptions, for any $c:\mathbb R\to r$ with $r$ finite there is an infinite $X\subseteq \mathbb R$ so that $c$ is constant on $X+X$. Comment: 12 pages, final version accepted for publication in the Proceedings of AMS (https://doi.org/10.1090/proc/14431). Paper 1129 on S. Shelah's list. Comments are very welcome |
| Databáze: | OpenAIRE |
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