{"paper":{"title":"An Intermediate Logic Contained in Medvedev's Logic with Disjunction Property","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Zhicheng Chen","submitted_at":"2025-02-24T15:19:10Z","abstract_excerpt":"Let $\\textbf{SU}$ be the superintuitionistic logic defined by the axiom $\\boldsymbol{su} = ((\\neg p\\to q)\\land(\\neg q\\to p) \\rightarrow r \\vee s) \\to ( p \\rightarrow r) \\vee(q \\rightarrow s)$, or equivalently, by Andrew's axiom. It is easy to check that $\\textbf{SU}$ is contained in Medvedev's logic and contains both Kreisel-Putnam logic and Scott logic. We show that on \\textbf{S4} frames, $\\boldsymbol{su}$ corresponds to a certain first-order property, called the ``strong union'' property. The strong completeness of \\textbf{SU}, with respect to the class of \\textbf{S4} frames enjoying this pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17242","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.17242/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"}