This is an announcement for the paper "Low distortion embeddings between $C(K)$ spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez. Abstract: We show that, for each ordinal $\alpha<\omega_1$, the space $C([0,\omega^\alpha])$ does not embed into $C(K)$ with distortion strictly less than $2$ unless $K^{(\alpha)}\neq \emptyset$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B85 Remarks: 11 pages Submitted from: antonin.prochazka@univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.0211 or http://arXiv.org/abs/1408.0211