{"paper":{"title":"Thin ultrafilters, P-hierarchu and MArtin Axiom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrzej Starosolski, Micha{\\l} Machura","submitted_at":"2012-01-09T10:19:48Z","abstract_excerpt":"Under MA we prove that for the ideal $\\cal I$ of thin sets on $\\omega$ and for any ordinal $\\gamma \\leq \\omega_1$ there is an ${\\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\\cal P}_{\\gamma}$ of P-hierarchy of ultrafilters. Since the class of ${\\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Fla\\v{s}kov\\'a, which states that there are ${\\cal I}$-ultrafilters which are not P-points. It is also related to theorem which states that under CH for any tall P-ideal $\\cal I$ on $\\omega$ there is an ${\\cal I}$-ultrafilter, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1725","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"}