{"paper":{"title":"Correspondences between model theory and Banach space theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.LO","authors_text":"Karim Khanaki","submitted_at":"2015-12-29T14:27:16Z","abstract_excerpt":"In \\cite{K3} we pointed out the correspondence between a result of Shelah in model theory, i.e. a theory is unstable if and only if it has IP or SOP, and the well known compactness theorem of Eberlein and \\v{S}mulian in functional analysis. In this paper, we relate a {\\em natural} Banach space $V$ to a formula $\\phi(x,y)$, and show that $\\phi$ is stable (resp NIP, NSOP) if and only if $V$ is reflexive (resp Rosenthal, weakly sequentially complete) Banach space. Also, we present a proof of the Eberlein-\\v{S}mulian theorem by a model theoretic approach using Ramsey theorems which is illustrative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08691","kind":"arxiv","version":2},"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"}