{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:49:55Z","timestamp":1773251395013,"version":"3.50.1"},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T00:00:00Z","timestamp":1179446400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce the relation of <jats:italic>almost\u2010reduction<\/jats:italic> in an arbitrary topological Ramsey space \u211b as a generalization of the relation of almost\u2010inclusion on \u2115<jats:sup>[\u221e]<\/jats:sup>. This leads us to a type of ultrafilter \ud835\udcb0 \u2286 \u211b which corresponds to the well\u2010known notion of <jats:italic>selective ultrafilter<\/jats:italic> on \u2115. The relationship turns out to be rather exact in the sense that it permits us to lift several well\u2010known facts about selective ultrafilters on \u2115 and the Ellentuck space \u2115<jats:sup>[\u221e]<\/jats:sup> to the ultrafilter \ud835\udcb0 and the Ramsey space \u211b. For example, we prove that the open coloring axiom holds on <jats:italic>L<\/jats:italic> (\u211d)[\ud835\udcb0], extending therefore the result from [3] which gives the same conclusion for the Ramsey space \u2115<jats:sup>[\u221e]<\/jats:sup>. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510045","type":"journal-article","created":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T22:44:52Z","timestamp":1179528292000},"page":"255-267","source":"Crossref","is-referenced-by-count":14,"title":["A notion of selective ultrafilter corresponding to topological Ramsey spaces"],"prefix":"10.1002","volume":"53","author":[{"given":"Jos\u00e9 G.","family":"Mijares","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,5,18]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"90","article-title":"Ultrafilters related to Hindman's finite\u2010unions theorem and its extensions","volume":"65","author":"Blass A.","year":"1987","journal-title":"Contemporary Mathematics"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"T. J.Carlson andS. G.Simpson Topological Ramsey theory. In: Mathematics of Ramsey Theory Algorithms and Combinatorics 5 (J. Ne\u015detr\u0302il and V. R\u00f6dl eds.) pp. 172\u2013183 (Springer\u2010Verlag 1990).","DOI":"10.1007\/978-3-642-72905-8_12"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1006\/aima.1998.1752","article-title":"Perfect\u2010set properties in L (\u211d)[\ud835\udcb0]","volume":"139","author":"Di Prisco C. A.","year":"1998","journal-title":"Advances in Mathematics"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272356"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300014054"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2154292"},{"key":"e_1_2_1_8_2","unstructured":"M.Goldstein Tools for your forcing construction. In: Set Theory of the Reals (H. Judah ed.) pp. 305\u2013360 Israel Math. Conf. Proc. Bar Ilan University 1993."},{"key":"e_1_2_1_9_2","first-page":"341","article-title":"The existence of certain ultrafilters on \u2115 and a conjecture of Graham and Rothschild","volume":"36","author":"Hindman N.","year":"1973","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90006-7"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(75)90039-4"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"e_1_2_1_13_2","unstructured":"S.Todorcevic andI.Farah Some Applications of the Method of Forcing (Yenisey 1995)."},{"key":"e_1_2_1_14_2","unstructured":"S.Todorcevic Introduction to Ramsey Spaces (Princeton University Press to appear)."},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","unstructured":"S.Todorcevic Partition Problems in Topology (Amer. Math. Soc. 1989).","DOI":"10.1090\/conm\/084"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510045","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T15:04:50Z","timestamp":1697641490000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,18]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1002\/malq.200510045"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510045","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,18]]}}}