{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T01:15:18Z","timestamp":1773105318588,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> Assume [Formula: see text]. Let [Formula: see text] be a [Formula: see text] equivalence relation coded in [Formula: see text]. [Formula: see text] has an ordinal definable equivalence class without any ordinal definable elements if and only if [Formula: see text] is unpinned. <\/jats:p><jats:p> [Formula: see text] proves [Formula: see text]-class section uniformization when [Formula: see text] is a [Formula: see text] equivalence relation on [Formula: see text] which is pinned in every transitive model of [Formula: see text] containing the real which codes [Formula: see text]: Suppose [Formula: see text] is a relation on [Formula: see text] such that each section [Formula: see text] is an [Formula: see text]-class, then there is a function [Formula: see text] such that for all [Formula: see text], [Formula: see text]. <\/jats:p><jats:p> [Formula: see text] proves that [Formula: see text] is J\u00f3nsson whenever [Formula: see text] is an ordinal: For every function [Formula: see text], there is an [Formula: see text] with [Formula: see text] in bijection with [Formula: see text] and [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061319500090","type":"journal-article","created":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T23:21:50Z","timestamp":1551655310000},"page":"1950009","source":"Crossref","is-referenced-by-count":8,"title":["Ordinal definability and combinatorics of equivalence relations"],"prefix":"10.1142","volume":"19","author":[{"given":"William","family":"Chan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Texas, Denton, 76203 TX, USA"}]}],"member":"219","published-online":{"date-parts":[[2019,10,2]]},"reference":[{"key":"S0219061319500090BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/533\/10510"},{"key":"S0219061319500090BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90010-7"},{"key":"S0219061319500090BIB004","first-page":"19","volume":"14","author":"Erd\u0151s P.","year":"1966","journal-title":"Bull. Acad. Polon. Sci. S\u00e9r. Sci. Math. Astronom. Phys."},{"key":"S0219061319500090BIB007","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2014.49"},{"key":"S0219061319500090BIB008","series-title":"Springer Monographs in Mathematics","volume-title":"Set Theory","author":"Jech T.","year":"2003"},{"key":"S0219061319500090BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/044"},{"key":"S0219061319500090BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-015-0436-9"},{"key":"S0219061319500090BIB012","doi-asserted-by":"publisher","DOI":"10.4064\/fm517-7-2018"},{"key":"S0219061319500090BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90012-0"},{"key":"S0219061319500090BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2016.08.018"},{"key":"S0219061319500090BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0069385"},{"issue":"2","key":"S0219061319500090BIB016","first-page":"281","volume":"39","author":"Neeman I.","year":"1998","journal-title":"Comment. Math. Univ. Carolin."},{"key":"S0219061319500090BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.09.014"},{"key":"S0219061319500090BIB018","doi-asserted-by":"publisher","DOI":"10.1515\/9783110213171"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061319500090","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T02:26:57Z","timestamp":1570069617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061319500090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,2]]},"references-count":14,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S0219061319500090"],"URL":"https:\/\/doi.org\/10.1142\/s0219061319500090","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,2]]}}}