{"paper":{"title":"Boundedness and absoluteness of some dynamical invariants in model theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN"],"primary_cat":"math.LO","authors_text":"Krzysztof Krupinski, Ludomir Newelski, Pierre Simon","submitted_at":"2017-04-29T09:21:54Z","abstract_excerpt":"Let ${\\mathfrak C}$ be a monster model of an arbitrary theory $T$, $\\bar \\alpha$ any tuple of bounded length of elements of ${\\mathfrak C}$, and $\\bar c$ an enumeration of all elements of ${\\mathfrak C}$. By $S_{\\bar \\alpha}({\\mathfrak C})$ denote the compact space of all complete types over ${\\mathfrak C}$ extending $tp(\\bar \\alpha/\\emptyset)$, and $S_{\\bar c}({\\mathfrak C})$ is defined analogously. Then $S_{\\bar \\alpha}({\\mathfrak C})$ and $S_{\\bar c}({\\mathfrak C})$ are naturally $Aut({\\mathfrak C})$-flows. We show that the Ellis groups of both these flows are of bounded size (i.e. smaller "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00159","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"}