{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:09:08Z","timestamp":1753884548770,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"NSF","award":["DMS1800323"],"award-info":[{"award-number":["DMS1800323"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p> We introduce the notion of [Formula: see text]-determinacy for [Formula: see text] a pointclass and [Formula: see text] an equivalence relation on a Polish space [Formula: see text]. A case of particular interest is the case when [Formula: see text] is the (left) shift-action of [Formula: see text] on [Formula: see text] where [Formula: see text] or [Formula: see text]. We show that for all shift actions by countable groups [Formula: see text], and any \u201creasonable\u201d pointclass [Formula: see text], that [Formula: see text]-determinacy implies [Formula: see text]-determinacy. We also prove a corresponding result when [Formula: see text] is a subshift of finite type of the shift map on [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061322500039","type":"journal-article","created":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T13:16:00Z","timestamp":1633526160000},"source":"Crossref","is-referenced-by-count":2,"title":["Equivalence relations and determinacy"],"prefix":"10.1142","volume":"22","author":[{"given":"Logan","family":"Crone","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203-5017, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lior","family":"Fishman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203-5017, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Jackson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203-5017, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,2,5]]},"reference":[{"key":"S0219061322500039BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1149121-0"},{"key":"S0219061322500039BIB002","doi-asserted-by":"publisher","DOI":"10.2307\/2273508"},{"key":"S0219061322500039BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0219061322500039BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/jams\/836"},{"key":"S0219061322500039BIB006","doi-asserted-by":"publisher","DOI":"10.2307\/1971035"},{"key":"S0219061322500039BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/042\/791065"},{"key":"S0219061322500039BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/155"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061322500039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T04:07:02Z","timestamp":1665374822000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061322500039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,5]]},"references-count":7,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["10.1142\/S0219061322500039"],"URL":"https:\/\/doi.org\/10.1142\/s0219061322500039","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2022,2,5]]},"article-number":"2250003"}}