{"paper":{"title":"On the structure of the set of higher order spreading models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B\\\"unyamin Sari, Konstantinos Tyros","submitted_at":"2013-10-21T05:31:30Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5429","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}