{"paper":{"title":"Forking in Short and Tame Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Rami Grossberg, Will Boney","submitted_at":"2013-06-27T16:21:45Z","abstract_excerpt":"We develop a notion of forking for Galois-types in the context of Abstract Elementary Classes (AECs). Under the hypotheses that an AEC $K$ is tame, type-short, and failure of an order-property, we consider\n  {\\bf Definition.} Let $M_0 \\prec N$ be models from $K$ and $A$ be a set. We say that the Galois-type of $A$ over $M$ \\emph{does not fork over $M_0$} iff for all small $a \\in A$ and all small $N^- \\prec N$, we have that Galois-type of $a$ over $N^-$ is realized in $M_0$.\n  Assuming property (E) (see Definition 3.3) we show that this non-forking is a well behaved notion of independence, in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6562","kind":"arxiv","version":11},"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"}