This is an announcement for the paper “On the Banach space structure of Banach lattices with disjointness preserving isometries: ultraroots and axiomatizability” by Yves Raynaud.

Abstract: Let $C$ be an axiomatizable class of order continuous real or complex Banach lattices, that is, this class is closed under isometric vector lattice isomorphisms and ultraproducts, and the complementary class is closed under ultrapowers. We show that if linear isometric embeddings of members of $C$ in their ultrapowers preserve disjointness, the class $C^B$ of Banach spaces obtained by forgetting the Banach lattice structure is still axiomatizable. Moreover if $C$ coincides with its "script class" $SC$, so does $C^B$ with $SC^B$. This allows us to give new examples of axiomatizable classes of Banach spaces, namely certain Musielak-Orlicz spaces, Nakano spaces, and mixed norm spaces.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.07510