This is an announcement for the paper "On the structure of the set of the higher order spreading models" by Bunyamin Sari and Konstantinos Tyros. Abstract: We generalize some results concerning the classical notion of a spreading model for the spreading models of order $\xi$. Among them, we prove that the set $SM_\xi^w(X)$ of the $\xi$-order spreading models of a Banach space $X$ generated by subordinated weakly null $\mathcal{F}$-sequences endowed with the pre-partial order of domination is a semi-lattice. Moreover, if $SM_\xi^w(X)$ contains an increasing sequence of length $\omega$ then it contains an increasing sequence of length $\omega_1$. Finally, if $SM_\xi^w(X)$ is uncountable, then it contains an antichain of size the continuum. Archive classification: math.FA Mathematics Subject Classification: 46B06, 46B25, 46B45 Remarks: 23 pages Submitted from: chcost@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.5429 or http://arXiv.org/abs/1310.5429