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Given subsets <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> of , we write  if there is a total computable function  satisfying for all , .<\/jats:p><jats:p>We shall discuss the central role  plays in this reducibility and its connection to strong\u2010hyper\u2010hyper\u2010immunity. We shall also compare agreement reducibility to other well\u2010known reducibilities, in particular s<jats:sub>1<\/jats:sub>\u2010 and s\u2010reducibility. We came upon this reducibility while studying the computable reducibility of a class of equivalence relations on  based on set\u2010agreement. We end by describing the origin of agreement reducibility and presenting some results in that\u00a0context.<\/jats:p>","DOI":"10.1002\/malq.201900088","type":"journal-article","created":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T23:48:44Z","timestamp":1610754524000},"page":"448-465","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Agreement reducibility"],"prefix":"10.1002","volume":"66","author":[{"given":"Rachel","family":"Epstein","sequence":"first","affiliation":[{"name":"Department of Mathematics Georgia College Milledgeville GA 31061 United States of America"}]},{"given":"Karen","family":"Lange","sequence":"additional","affiliation":[{"name":"Department of Mathematics Wellesley College 106 Central Street Wellesley MA 02481 United States of America"}]}],"member":"311","published-online":{"date-parts":[[2021,1,15]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2013.8"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273443"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:ALLO.0000048827.30718.2c"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1146620059"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201600045"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0216-5"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272750"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086114"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.3233\/COM-2012-004"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68441-3"},{"key":"e_1_2_6_12_1","volume-title":"\u0422\u0435\u043e\u0440\u0438\u044f \u043d\u0443\u043c\u0435\u0440\u0430\u0446\u0438\u0439, \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u041b\u043e\u0433\u0438\u043a\u0430 \u0438 \u041e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438","author":"Ershov Y. 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