{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T21:02:35Z","timestamp":1694466155447},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T00:00:00Z","timestamp":1554854400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371203"],"award-info":[{"award-number":["11371203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2019,5]]},"abstract":"Abstract<\/jats:title>Let X<\/jats:italic>, Y<\/jats:italic> be Polish spaces, , . We say A<\/jats:italic> is universal for \u0393 provided that each x<\/jats:italic>\u2010section of A<\/jats:italic> is in \u0393 and each element of \u0393 occurs as an x<\/jats:italic>\u2010section of A<\/jats:italic>. An equivalence relation generated by a set is denoted by , where . The following results are shown:\n\nIf A<\/jats:italic> is a set universal for all nonempty closed subsets of Y<\/jats:italic>, then is a equivalence relation and .<\/jats:p><\/jats:list-item>\nIf A<\/jats:italic> is a set universal for all countable subsets of Y<\/jats:italic>, then is a equivalence relation,\u00a0and\n\n and ;<\/jats:p><\/jats:list-item>\nif , then ;<\/jats:p><\/jats:list-item>\nif every set is Lebesgue measurable or has the Baire property, then .<\/jats:p><\/jats:list-item>\nfor , if every set has the Baire property, and E<\/jats:italic> is any equivalence relation, then .<\/jats:p><\/jats:list-item>\n<\/jats:list><\/jats:p><\/jats:list-item><\/jats:list><\/jats:p>","DOI":"10.1002\/malq.201700066","type":"journal-article","created":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T08:04:49Z","timestamp":1554883489000},"page":"8-13","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reductions on equivalence relations generated by universal sets"],"prefix":"10.1002","volume":"65","author":[{"given":"Longyun","family":"Ding","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences & Key Laboratory for Pure Mathematics and Combinatorics (LPMC) of the Ministry of Education Nankai University 94 Weijin Road Tianjin 300071 People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences & Key Laboratory for Pure Mathematics and Combinatorics (LPMC) of the Ministry of Education Nankai University 94 Weijin Road Tianjin 300071 People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,4,10]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1988-0947685-3"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781584887942"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-07-04243-2"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2012.05.015"},{"key":"e_1_2_5_7_1","volume-title":"Descriptive Set Theory","author":"Moschovakis Y. 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