{"paper":{"title":"On the Intermediate Models of Strongly Compact Prikry Forcing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A simple combinatorial property characterizes all projections of the strongly compact Prikry forcing using κ-complete fine measures.","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ben-Zion Weltsch, Sebastiano Thei, Tom Benhamou","submitted_at":"2026-05-09T20:47:44Z","abstract_excerpt":"We analyze the intermediate models of the strongly compact Prikry forcing. We exhibit a simple combinatorial property which, for a given supercompact cardinal $\\kappa$, characterize the projections of all projections of the strongly compact Prikry forcing using $\\kappa$-complete fine measures. Considering level-by-level results, if $\\kappa$ is $2^\\lambda$-strongly compact, we characterize the forcings of size $\\leq\\lambda$ which are projections of that $\\lambda$-strongly compact Prikry forcing. Our characterization generalizes several known results, including those of Benhamou-Hayut-Gitik and "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We exhibit a simple combinatorial property which, for a given supercompact cardinal κ, characterize the projections of all projections of the strongly compact Prikry forcing using κ-complete fine measures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The existence of a κ-complete fine measure U on P_κ(λ) (or the assumption that κ is 2^λ-strongly compact) together with the standard properties of Prikry forcing conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The authors characterize projections of strongly compact Prikry forcing using κ-complete fine measures, generalize prior results on κ-distributive forcings, and give Rudin-Keisler-style criteria for projections.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A simple combinatorial property characterizes all projections of the strongly compact Prikry forcing using κ-complete fine measures.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"669ac510e9d7488b3dae4eb279ba7661d5b1093b7e16b2de7d0ce1185e3af479"},"source":{"id":"2605.09161","kind":"arxiv","version":2},"verdict":{"id":"4a0d3505-ad48-4907-b356-f58d80850926","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:32:23.994649Z","strongest_claim":"We exhibit a simple combinatorial property which, for a given supercompact cardinal κ, characterize the projections of all projections of the strongly compact Prikry forcing using κ-complete fine measures.","one_line_summary":"The authors characterize projections of strongly compact Prikry forcing using κ-complete fine measures, generalize prior results on κ-distributive forcings, and give Rudin-Keisler-style criteria for projections.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The existence of a κ-complete fine measure U on P_κ(λ) (or the assumption that κ is 2^λ-strongly compact) together with the standard properties of Prikry forcing conditions.","pith_extraction_headline":"A simple combinatorial property characterizes all projections of the strongly compact Prikry forcing using κ-complete fine measures."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09161/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T08:22:01.614291Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:36:27.243862Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:31:18.573667Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:29:35.457865Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"9291f5ab9bcd9fbd06126b81da519af584ab7901c851083dcbfef97b27e4e708"},"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"}