{"paper":{"title":"All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.GR","math.LO"],"primary_cat":"math.CO","authors_text":"Jan Hubi\\v{c}ka, Jaroslav Ne\\v{s}et\\v{r}il, Mat\\v{e}j Kone\\v{c}n\\'y","submitted_at":"2019-02-11T13:10:55Z","abstract_excerpt":"In this paper we prove a general theorem showing the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for classes of structures containing relations and unary functions, optionally equipped with a permutation group of the language. The proof is elementary, combinatorial and fully self-contained. Our result is a common strengthening of the Herwig-Lascar theorem on EPPA for relational classes with forbidden homomorphisms, the Hodkinson-Otto theorem on EPPA for relational free amalgamation classes, its strengthening for unary functions by Evans, Hubi\\v{c}ka"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03855","kind":"arxiv","version":4},"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/1902.03855/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"}