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)

@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}
}