This is an announcement for the paper "Saturated extensions, the attractors method and Hereditarily James Tree Space" by Spiros A. Argyros, Alexander D. Arvanitakis, and Andreas G. Tolias. Abstract: In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors. Archive classification: math.FA The source file(s), Aat6.tex: 290045 bytes, is(are) stored in gzipped form as 0807.2392.gz with size 77kb. The corresponding postcript file has gzipped size 377kb. Submitted from: sargyros@math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2392 or http://arXiv.org/abs/0807.2392 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2392 or in gzipped form by using subject line get 0807.2392 to: math@arXiv.org.