This is an announcement for the paper "Borel reducibility and Holder($\alpha$) embeddability between Banach spaces" by Longyun Ding. Abstract: We investigate Borel reducibility between equivalence relations $E(X,p)=X^{\Bbb N}/\ell_p(X)$'s where $X$ is a separable Banach space. We show that this reducibility is related to the so called H\"older$(\alpha)$ embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between $E(L_r,p)$'s and $E(c_0,p)$'s for $r,p\in[1,+\infty)$. We also answer a problem presented by Kanovei in the affirmative by showing that $C({\Bbb R}^+)/C_0({\Bbb R}^+)$ is Borel bireducible to ${\Bbb R}^{\Bbb N}/c_0$. Archive classification: math.LO math.FA Mathematics Subject Classification: 03E15, 46B20, 47H99 Remarks: 29 pages The source file(s), Banach.tex: 57984 bytes, is(are) stored in gzipped form as 0912.1912.gz with size 16kb. The corresponding postcript file has gzipped size 128kb. Submitted from: dingly@nankai.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.1912 or http://arXiv.org/abs/0912.1912 or by email in unzipped form by transmitting an empty message with subject line uget 0912.1912 or in gzipped form by using subject line get 0912.1912 to: math@arXiv.org.