A solution to the problem of the existence of a dense plastic subset $X\subseteq\mathbb{R}$ of cardinality $|X|<\frak{c}$

Abstract

Under the assumption $\frak{c}\geqslant \omega_2$, we give an example of a dense plastic subset $X\subseteq\mathbb{R}$ of cardinality $|X|<\frak{c}$. This answers Problem 1 of arXiv:2510.10537.