MA or PFA as substitutes for CH in the non-plasticity conclusion for small dense subsets of ℝ

Ascertain whether Martin’s Axiom (MA) or the Proper Forcing Axiom (PFA) suffices to imply that every dense subset X of the real line with cardinality |X| < 𝔠 is not plastic, thereby replacing the CH assumption in Corollary 4.

Background

Corollary 4 derives the non-plasticity of small dense subsets of ℝ under CH. The authors discuss whether other set-theoretic assumptions could ensure the same conclusion, noting known logical relationships among CH, MA, and PFA (both CH and PFA imply MA, and PFA is incompatible with CH).

The question asks if MA or PFA alone provide sufficient strength to establish the non-plasticity of dense subsets of ℝ of size less than the continuum, in the absence of CH.