{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:34:32Z","timestamp":1773146072645,"version":"3.50.1"},"reference-count":13,"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":3571,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>In this paper we introduce a new property of families of functions on the Baire space, called pseudo-dominating, and apply the properties of these families to the study of cardinal characteristics of the continuum. We show that the minimum cardinality of a pseudo-dominating family is min {<jats:italic>\u03c4, \u2202<\/jats:italic>}. We derive two corollaries from the proof:<jats:italic>\u03c4<\/jats:italic>\u2265 min{<jats:italic>\u2202, u<\/jats:italic>} and min{<jats:italic>\u2202, \u03c4<\/jats:italic>} = min{<jats:italic>\u2202, \u03c4<jats:sub>\u03c3<\/jats:sub><\/jats:italic>}. We show that if a dominating family is partitioned into fewer that s pieces, then one of the pieces is pseudo-dominating. We finally show that<jats:italic>u<\/jats:italic>&lt;<jats:italic>g<\/jats:italic>implies that every unbounded family of functions is pseudo-dominating, and that the Filter Dichotomy principle is equivalent to every unbounded family of functions being finitely pseudo-dominating.<\/jats:p>","DOI":"10.2178\/jsl\/1082418539","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:36:43Z","timestamp":1109799403000},"page":"482-498","source":"Crossref","is-referenced-by-count":7,"title":["Combinatorics for the dominating and unsplitting numbers"],"prefix":"10.1017","volume":"69","author":[{"given":"Jason","family":"Aubrey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200007866_ref005","first-page":"50","volume":"54","author":"Blass","year":"1989","journal-title":"Consistency results about filters and the number of inequivalent growth types"},{"key":"S0022481200007866_ref013","doi-asserted-by":"publisher","DOI":"10.4064\/sm-67-1-13-43"},{"key":"S0022481200007866_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1028761-1"},{"key":"S0022481200007866_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/302\/05060"},{"key":"S0022481200007866_ref002","unstructured":"Blass Andreas , Combinatorial cardinal characteristics of the continuum, Handbook of Set Theory ( Foreman Matthew , Kanimori Akihiro , and Magidor Menachem , editors), Kluwer, to appear."},{"key":"S0022481200007866_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01793782"},{"key":"S0022481200007866_ref006","first-page":"727","volume":"64","author":"Blass","year":"1999","journal-title":"On the cofinality of ultrapowers"},{"key":"S0022481200007866_ref007","first-page":"269","article-title":"Around splitting and reaping","volume":"39","author":"Brendle","year":"1998","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481200007866_ref008","first-page":"92","article-title":"On the existence of P-points in the Stone-\u010cech compactification of the integers","volume":"92","author":"Ketone","year":"1976","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200007866_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s001530000049"},{"key":"S0022481200007866_ref011","unstructured":"Nyikos Peter , Special ultrafilters and cofinal subsets of \u03c9\u03c9, to appear."},{"key":"S0022481200007866_ref012","doi-asserted-by":"crossref","first-page":"556","DOI":"10.21136\/CMJ.1977.101493","article-title":"Families of sets and functions","volume":"27","author":"Solomon","year":"1977","journal-title":"Czechoslovak Mathematical Journal"},{"key":"S0022481200007866_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(91)90105-U"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007866","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T06:16:37Z","timestamp":1625552197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007866\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,6]]}},"alternative-id":["S0022481200007866"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1082418539","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6]]}}}