{"paper":{"title":"The Sch\\\"utzenberger product for syntactic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.GN","math.LO"],"primary_cat":"cs.LO","authors_text":"Daniela Petrisan, Luca Reggio, Mai Gehrke","submitted_at":"2016-03-27T22:27:49Z","abstract_excerpt":"Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers for arbitrary formal languages of finite words over finite alphabets. This leads to a setting that is well-suited for applying existing tools from Stone duality as applied in semantics. The main focus of the paper is the development of topo-algebraic constructions pertinent to the treatment of languages given by logic formulas. In particular, using the standard semantic view of quantification as projection, we deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08264","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":""},"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"}