{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T08:29:20Z","timestamp":1685003360688},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":741,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A metric space (<jats:italic>X, d<\/jats:italic>) is<jats:italic>monotone<\/jats:italic>if there is a linear order &lt; on<jats:italic>X<\/jats:italic>and a constant<jats:italic>c<\/jats:italic>such that<jats:italic>d(x, y)<\/jats:italic>\u2264<jats:italic>c d(x, z)<\/jats:italic>for all<jats:italic>x<\/jats:italic>&lt;<jats:italic>y<\/jats:italic>&lt;<jats:italic>z<\/jats:italic>in<jats:italic>X<\/jats:italic>. We investigate cardinal invariants of the<jats:italic>\u03c3<\/jats:italic>-ideal<jats:bold>Mon<\/jats:bold>generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated. In particular, we show that non(<jats:bold>Mon<\/jats:bold>) \u2265<jats:italic>m<\/jats:italic><jats:sub><jats:italic>\u03c3<\/jats:italic>-linked<\/jats:sub>, but non(<jats:bold>Mon<\/jats:bold>) &lt;<jats:italic>m<\/jats:italic><jats:sub><jats:italic>\u03c3<\/jats:italic>-centered<\/jats:sub>is consistent. Also cov(<jats:bold>Mon<\/jats:bold>) &lt;<jats:italic>c<\/jats:italic>and cof (<jats:italic>N<\/jats:italic>) &lt; cov(<jats:bold>Mon<\/jats:bold>) are consistent.<\/jats:p>","DOI":"10.2178\/jsl\/1327068697","type":"journal-article","created":{"date-parts":[[2012,1,20]],"date-time":"2012-01-20T14:16:13Z","timestamp":1327068973000},"page":"159-173","source":"Crossref","is-referenced-by-count":4,"title":["Cardinal invariants of monotone and porous sets"],"prefix":"10.1017","volume":"77","author":[{"given":"Michael","family":"Hru\u0161\u00e1k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ond\u0159ej","family":"Zindulka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000979_ref017","first-page":"509","volume-title":"Abstract and Applied Analysis","author":"Zaj\u00ed\u010dek","year":"2005"},{"key":"S0022481200000979_ref021","doi-asserted-by":"publisher","DOI":"10.14321\/realanalexch.30.2.0547"},{"key":"S0022481200000979_ref015","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-62.2.353"},{"key":"S0022481200000979_ref013","first-page":"433","volume-title":"Set theory of the reals (Ramat Gan, 1991), Israel mathematics conference proceedings","volume":"6","author":"Repick\u00fd","year":"1993"},{"key":"S0022481200000979_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623813"},{"key":"S0022481200000979_ref019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542732"},{"key":"S0022481200000979_ref020","doi-asserted-by":"publisher","DOI":"10.4064\/fm204-2-4"},{"key":"S0022481200000979_ref004","first-page":"861","article-title":"OCA and towers in (N) \/fin","volume":"37","author":"Farah","year":"1996","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481200000979_ref010","volume-title":"Order","author":"Nekvinda"},{"key":"S0022481200000979_ref005","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-14978"},{"key":"S0022481200000979_ref012","doi-asserted-by":"crossref","first-page":"340","DOI":"10.2307\/44153705","article-title":"Additivity of porous sets","volume":"16","author":"Repick\u00fd","year":"1990","journal-title":"Real Analysis Exchange"},{"key":"S0022481200000979_ref006","volume-title":"Set theory","volume":"102","author":"Kunen","year":"1980"},{"key":"S0022481200000979_ref007","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-38.1.125"},{"key":"S0022481200000979_ref023","volume-title":"Fundamenta Mathematicae","author":"Zindulka"},{"key":"S0022481200000979_ref001","doi-asserted-by":"crossref","DOI":"10.1201\/9781439863466","volume-title":"Set theory","author":"Bartoszy\u0144ski","year":"1995"},{"key":"S0022481200000979_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-02992-9"},{"key":"S0022481200000979_ref011","doi-asserted-by":"crossref","first-page":"282","DOI":"10.2307\/44152006","article-title":"Porous sets and additivity of Lebesgue measure","volume":"15","author":"Repick\u00fd","year":"1989","journal-title":"Real Analysis Exchange"},{"key":"S0022481200000979_ref009","doi-asserted-by":"publisher","DOI":"10.4064\/fm213-3-3"},{"key":"S0022481200000979_ref014","doi-asserted-by":"publisher","DOI":"10.14321\/realanalexch.32.1.0055"},{"key":"S0022481200000979_ref016","doi-asserted-by":"crossref","first-page":"314","DOI":"10.2307\/44151885","volume":"13","author":"Zaj\u00ed\u010dek","year":"1987","journal-title":"Real Analysis Exchange"},{"key":"S0022481200000979_ref018","first-page":"221","volume-title":"Abstract and Applied Analysis","author":"Zaj\u00ed\u010dek","year":"2005"},{"key":"S0022481200000979_ref022","doi-asserted-by":"publisher","DOI":"10.4064\/fm185-1-2"},{"key":"S0022481200000979_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90082-0"},{"key":"S0022481200000979_ref024","unstructured":"Zindulka Ond\u0159ej , Mapping Borel sets onto balls by Lipschitz and nearly Lipschitz maps, in preparation."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T03:45:52Z","timestamp":1593575152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000979\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0022481200000979"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1327068697","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3]]}}}