Infinite monochromatic sumsets for colourings of the reals

Péter Komjáth; Imre Leader; Paul A. Russell; Saharon Shelah; Daniel Tamas Soukup; Zoltán Vidnyánszky

doi:10.1090/proc/14431

Infinite monochromatic sumsets for colourings of the reals

Péter Komjáth
, Imre Leader
, Paul A. Russell
, Saharon Shelah
, Daniel Tamas Soukup
, Zoltán Vidnyánszky

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

N. Hindman, I. Leader, and D. Strauss proved that it is consistent that there is a finite colouring of R so that no infinite sumset X + 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 finite colouring c of R there is an infinite X ⊆ R so that c ↾ X + X is constant.

Original language	English
Pages (from-to)	2673-2684
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	6
DOIs	https://doi.org/10.1090/proc/14431
Publication status	Published - 2019

Austrian Fields of Science 2012

101012 Combinatorics

Keywords

Sumset
colouring
continuum
monochromatic
partition relation
Continuum
Partition relation
Colouring
Monochromatic

Access to Document

10.1090/proc/14431

Cite this

@article{f140fa1fa1204810b12dfe27761e52c4,

title = "Infinite monochromatic sumsets for colourings of the reals",

abstract = "N. Hindman, I. Leader, and D. Strauss proved that it is consistent that there is a finite colouring of R so that no infinite sumset X + 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 finite colouring c of R there is an infinite X ⊆ R so that c ↾ X + X is constant.",

keywords = "Sumset, colouring, continuum, monochromatic, partition relation, Continuum, Partition relation, Colouring, Monochromatic",

author = "P{\'e}ter Komj{\'a}th and Imre Leader and Russell, \{Paul A.\} and Saharon Shelah and Soukup, \{Daniel Tamas\} and Zolt{\'a}n Vidny{\'a}nszky",

note = "Publisher Copyright: {\textcopyright} 2019 Amerian Mathematial Soiety.",

year = "2019",

doi = "10.1090/proc/14431",

language = "English",

volume = "147",

pages = "2673--2684",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "6",

}

TY - JOUR

T1 - Infinite monochromatic sumsets for colourings of the reals

AU - Komjáth, Péter

AU - Leader, Imre

AU - Russell, Paul A.

AU - Shelah, Saharon

AU - Soukup, Daniel Tamas

AU - Vidnyánszky, Zoltán

PY - 2019

Y1 - 2019

N2 - N. Hindman, I. Leader, and D. Strauss proved that it is consistent that there is a finite colouring of R so that no infinite sumset X + 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 finite colouring c of R there is an infinite X ⊆ R so that c ↾ X + X is constant.

AB - N. Hindman, I. Leader, and D. Strauss proved that it is consistent that there is a finite colouring of R so that no infinite sumset X + 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 finite colouring c of R there is an infinite X ⊆ R so that c ↾ X + X is constant.

KW - Sumset

KW - colouring

KW - continuum

KW - monochromatic

KW - partition relation

KW - Continuum

KW - Partition relation

KW - Colouring

KW - Monochromatic

UR - https://www.scopus.com/pages/publications/85071937390

U2 - 10.1090/proc/14431

DO - 10.1090/proc/14431

M3 - Article

SN - 0002-9939

VL - 147

SP - 2673

EP - 2684

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Infinite monochromatic sumsets for colourings of the reals

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Cite this