{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T05:41:38Z","timestamp":1697175698016},"reference-count":10,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T00:00:00Z","timestamp":1123027200000},"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":[[2005,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove a partition theorem for analytic sets, namely, if <jats:italic>X<\/jats:italic> is an analytic set in a Polish space and [<jats:italic>X<\/jats:italic>]<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> = <jats:italic>K<\/jats:italic><jats:sub>0<\/jats:sub> \u222a <jats:italic>K<\/jats:italic><jats:sub>1<\/jats:sub> with <jats:italic>K<\/jats:italic><jats:sub>0<\/jats:sub> open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect <jats:italic>K<\/jats:italic><jats:sub>0<\/jats:sub>\u2010homogeneous subset or <jats:italic>X<\/jats:italic> is a countable union of <jats:italic>K<\/jats:italic><jats:sub>1<\/jats:sub>\u2010homogeneous subsets. We also prove a partition theorem for analytic sets in the three\u2010dimensional case. Finally, we give some applications of the theorems. (\u00a9 2005 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510003","type":"journal-article","created":{"date-parts":[[2005,8,3]],"date-time":"2005-08-03T20:53:18Z","timestamp":1123102398000},"page":"462-469","source":"Crossref","is-referenced-by-count":0,"title":["A high dimensional Open Coloring Axiom"],"prefix":"10.1002","volume":"51","author":[{"given":"Bin","family":"He","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,8,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1090\/S0002-9939-1981-0609665-0","article-title":"A partition theorem for perfect sets","volume":"82","author":"Blass A.","year":"1981","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"F.von Engelen K.Kunen andA.Miller Two remarks about analytic sets. In: Lecture Notes in Mathematics 1401 pp. 68\u201372 (Springer\u2010Verlag Berlin 1989).","DOI":"10.1007\/BFb0097332"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2154292"},{"key":"e_1_2_1_5_2","unstructured":"T.Jech Set Theory (Academic Press New York 1978)."},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"A. S.Kechris Classical Descriptive Set Theory (Springer\u2010Verlag New York 1994).","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"A.Miller Descriptive Set Theory and Forcing (Springer\u2010Verlag Berlin 1995).","DOI":"10.1007\/978-3-662-21773-3"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275926"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"S.Todor\u010devi\u0107 Partition problems in topology. Contemporary Mathematics 84 (AMS Providence 1989).","DOI":"10.1090\/conm\/084"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"B.Veli\u010dkovi\u0107 Applications of the Open Coloring Axiom. In: Set Theory of the Continuum (H. Judah W. Just W. H. Woodin eds.) pp. 137\u2013154 (Springer\u2010Verlag Berlin 1992).","DOI":"10.1007\/978-1-4613-9754-0_12"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(93)90127-Y"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510003","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T10:58:10Z","timestamp":1697108290000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,3]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1002\/malq.200510003"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510003","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,3]]}}}