Monochromatic Sumset Without the use of large cardinals

We show in this note that in the forcing extension by $Add(\omega ,{\mathrm{\beth }}_{\omega })$, the following Ramsey property holds: for any $r\in \omega$ and any $f:\mathbb{R}\to r$, there exists an infinite $X\subset $\mathbb{R}$$suchthat$X+X$ismonochromaticunder$f$. We also show the Ramsey statement above is true in $\mathrm{Z}\mathrm{F}\mathrm{C}$ when $r=2$. This answers two questions by Komj'ath, Leader, Russell, Shelah, Soukup and Vidny'anszky.