# Sh:1129

- Komjáth, P., Leader, I., Russell, P., Shelah, S., Soukup, D. T., & Vidnyánszky, Z. (2019).
*Infinite monochromatic sumsets for colourings of the reals*. Proc. Amer. Math. Soc.,**147**(6), 2673–2684. arXiv: 1710.07500 DOI: 10.1090/proc/14431 MR: 3951442 -
Abstract:

N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite coloring of \mathbb{R} so that no infinite sumset X + X is monochromatic. The (rather fascinating) question if the same conclusion holds in ZFC was open until now: 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\upharpoonright X + X is constant. - published version (12p)

Bib entry

@article{Sh:1129, author = {Komj{\'a}th, P{\'e}ter and Leader, Imre and Russell, Paul and Shelah, Saharon and Soukup, D{\'a}niel Tam{\'a}s and Vidny{\'a}nszky, Zolt{\'a}n}, title = {{Infinite monochromatic sumsets for colourings of the reals}}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {147}, number = {6}, year = {2019}, pages = {2673--2684}, issn = {0002-9939}, mrnumber = {3951442}, mrclass = {03E02 (03E35 05D10)}, doi = {10.1090/proc/14431}, note = {\href{https://arxiv.org/abs/1710.07500}{arXiv: 1710.07500}}, arxiv_number = {1710.07500} }