This is an announcement for the paper "The cofinal property of the reflexive indecomposable Banach spaces" by Spiros A. Argyros and Theocharis Raikoftsalis. Abstract: It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell_p$ saturated space with $1<p<\infty$ and of a $c_0$ saturated space. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B06, 46B70 Remarks: 29 pages The source file(s), Arg-Raiko-Cofinal.tex: 122453 bytes, is(are) stored in gzipped form as 1003.0870.gz with size 36kb. The corresponding postcript file has gzipped size 84kb. Submitted from: sargyros@math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.0870 or http://arXiv.org/abs/1003.0870 or by email in unzipped form by transmitting an empty message with subject line uget 1003.0870 or in gzipped form by using subject line get 1003.0870 to: math@arXiv.org.