This is an announcement for the paper "On spaces admitting no $\ell_p$ or $c_0$ spreading model" by Spiros A. Argyros and Kevin Beanland. Abstract: It is shown that for each separable Banach space $X$ not admitting $\ell_1$ as a spreading model there is a space $Y$ having $X$ as a quotient and not admitting any $\ell_p$ for $1 \leq p < \infty$ or $c_0$ as a spreading model. We also include the solution to a question of W.B. Johnson and H.P. Rosenthal on the existence of a separable space not admitting as a quotient any space with separable dual. Archive classification: math.FA Mathematics Subject Classification: 46B06 Remarks: 17 pages Submitted from: kbeanland@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.4714 or http://arXiv.org/abs/1111.4714