{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:18:40Z","timestamp":1773249520587,"version":"3.50.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1380,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the pair-splitting number<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002711_inline1\"\/>which is a variation of splitting number, pair-reaping number<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002711_inline2\"\/>which is a variation of reaping number and cardinal invariants of ideals on \u03c9. We also study cardinal invariants of<jats:italic>F<\/jats:italic>\u03c3 ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Kat\u011btov-minimal among ideals not satisfying Fatou's lemma.<\/jats:p>","DOI":"10.2178\/jsl\/1268917498","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"661-677","source":"Crossref","is-referenced-by-count":18,"title":["Pair-splitting, pair-reaping and cardinal invariants of<i>F<\/i>\u03c3-ideals"],"prefix":"10.1017","volume":"75","author":[{"given":"Michael","family":"Hru\u0161\u00e1k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Meza-Alc\u00e1ntara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroaki","family":"Minami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002711_ref015","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4064\/fm-163-3-215-228","article-title":"Filters and sequences","volume":"163","author":"Solecki","year":"2000","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200002711_ref014","unstructured":"Minami Hiroaki , On pair-splitting and pair-reaping pairs of \u03c9, preprint."},{"key":"S0022481200002711_ref013","unstructured":"Minami Hiroaki , Around splitting and reaping number for partitions of \u03c9, submitted 08 2007."},{"key":"S0022481200002711_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1992-1068126-5"},{"key":"S0022481200002711_ref006","first-page":"1337","volume":"68","author":"Hru\u0161\u00e1k","year":"2003","journal-title":"Ordering MAD families a la Kat\u00e9tov"},{"key":"S0022481200002711_ref008","first-page":"247","volume":"66","author":"Kurili\u0107","year":"2001","journal-title":"Cohen-stable families of subsets of integers"},{"key":"S0022481200002711_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm183-1-4"},{"key":"S0022481200002711_ref003","volume-title":"Handbook of set theory","author":"Blass"},{"key":"S0022481200002711_ref016","first-page":"619","volume-title":"Set theory of the reals","volume":"6","author":"Vojt\u00e1\u0161","year":"1993"},{"key":"S0022481200002711_ref002","doi-asserted-by":"crossref","DOI":"10.1201\/9781439863466","volume-title":"Set theory. On the structure of the real line","author":"Bartoszy\u0144ski","year":"1995"},{"key":"S0022481200002711_ref011","first-page":"1179","volume":"62","author":"Mildenberger","year":"1997","journal-title":"Non-constructive Galois\u2013Tukey connections"},{"key":"S0022481200002711_ref007","first-page":"1713","volume":"65","author":"Kada","year":"2000","journal-title":"More on Cicho\u0144's diagram and infinite games"},{"key":"S0022481200002711_ref012","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200211)48:4<517::AID-MALQ517>3.0.CO;2-#"},{"key":"S0022481200002711_ref005","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2007-024-8"},{"key":"S0022481200002711_ref004","first-page":"305","volume-title":"Set theory of the reals","volume":"6","author":"Goldstern","year":"1991"},{"key":"S0022481200002711_ref010","doi-asserted-by":"publisher","DOI":"10.4064\/fm-138-2-103-111"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002711","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,24]],"date-time":"2021-10-24T23:43:41Z","timestamp":1635119021000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002711\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["S0022481200002711"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1268917498","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}