{"paper":{"title":"Combinatorics of Schur ultrafilters","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Schur ultrafilters on countable commutative groups have a combinatorial characterization that permits constructing a free non-infinitary example on the integers and a free Schur P-point under the continuum hypothesis.","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"S. Bardyla","submitted_at":"2026-05-17T12:14:30Z","abstract_excerpt":"In this paper, we provide a combinatorial characterization of the elements of Schur ultrafilters on countable commutative groups. Using this characterization, we construct a free Schur ultrafilter on $\\mathbb Z$ that is not infinitary Schur. Moreover, assuming the Continuum Hypothesis, we establish the existence of a free Schur P-point on $\\mathbb Z$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide a combinatorial characterization of the elements of Schur ultrafilters on countable commutative groups. Using this characterization, we construct a free Schur ultrafilter on Z that is not infinitary Schur. 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Using this characterization, we construct a free Schur ultrafilter on Z that is not infinitary Schur. Moreover, assuming the Continuum Hypothesis, we establish the existence of a free Schur P-point on Z.","one_line_summary":"Combinatorial characterization of Schur ultrafilters on countable commutative groups, plus construction of a free non-infinitary Schur ultrafilter on Z and existence of a free Schur P-point on Z under CH.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Continuum Hypothesis is assumed to obtain the free Schur P-point on Z; the combinatorial characterization itself is taken as the basis for the explicit construction on Z.","pith_extraction_headline":"Schur ultrafilters on countable commutative groups have a combinatorial characterization that permits constructing a free non-infinitary example on the integers and a free Schur P-point under the continuum hypothesis."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17411/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.624184Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:52:12.572797Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.745682Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.690245Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ea7b037f7d3e1f60602dc3cf7f435fd5ff8f4b787cb71a12be350d89c5b6eefa"},"references":{"count":9,"sample":[{"doi":"","year":2025,"title":"S. 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