This is an announcement for the paper "A c_0-saturated Banach space with no long unconditional basic sequences" by Jordi Lopez Abad and Stevo Todorcevic. Abstract: We present a Banach space $\mathfrak X$ with a Schauder basis of length $\omega\_1$ which is saturated by copies of $c\_0$ and such that for every closed decomposition of a closed subspace $X=X\_0\oplus X\_1$, either $X\_0$ or $X\_1$ has to be separable. This can be considered as the non-separable counterpart of the notion of hereditarily indecomposable space. Indeed, the subspaces of $\mathfrak X$ have ``few operators'' in the sense that every bounded operator $T:X \rightarrow \mathfrak{X}$ from a subspace $X$ of $\mathfrak{X}$ into $\mathfrak{X}$ is the sum of a multiple of the inclusion and a $\omega\_1$-singular operator, i.e., an operator $S$ which is not an isomorphism on any non-separable subspace of $X$. We also show that while $\mathfrak{X}$ is not distortable (being $c\_0$-saturated), it is arbitrarily $\omega\_1$-distortable in the sense that for every $\lambda>1$ there is an equivalent norm $\||\cdot \||$ on $\mathfrak{X}$ such that for every non-separable subspace $X$ of $\mathfrak{X}$ there are $x,y\in S\_X$ such that $\||\cdot \|| / \||\cdot \||\ge \la$. Archive classification: Functional Analysis; Logic Mathematics Subject Classification: MSC Primary 46B20, 03E02; Secondary 46B26, 46B28 The source file(s), c0s-ouhi.tex: 63870 bytes, is(are) stored in gzipped form as 0610562.gz with size 19kb. The corresponding postcript file has gzipped size 84kb. Submitted from: abad@logique.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0610562 or http://arXiv.org/abs/math.FA/0610562 or by email in unzipped form by transmitting an empty message with subject line uget 0610562 or in gzipped form by using subject line get 0610562 to: math@arXiv.org.