{"paper":{"title":"Existentially closed measure-preserving actions of approximately treeable groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.LO","authors_text":"Brandon Seward, Isaac Goldbring, Robin Tucker-Drob","submitted_at":"2025-07-03T22:05:11Z","abstract_excerpt":"Given a countable group $\\Gamma$, letting $\\mathcal{K}_\\Gamma$ denote the class of {\\pmp} actions of $\\Gamma$, we study the question of when the model companion of $\\mathcal{K}_\\Gamma$ exists. Berenstein, Henson, and Ibarluc\\'ia showed that the model companion of $\\mathcal{K}_\\Gamma$ exists when $\\Gamma$ is a nonabelian free group on a countable number of generators. We significantly generalize their result by showing that the model companion of $\\cal K_\\Gamma$ exists whenever $\\Gamma$ is an approximately treeable group. The class of approximately treeable groups contain the class of treeable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03195","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.03195/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}