{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T11:33:55Z","timestamp":1773142435606,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","funder":[{"name":"NSF","award":["DMS-1703708"],"award-info":[{"award-number":["DMS-1703708"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p> If [Formula: see text] is a proper Polish metric space and [Formula: see text] is any countable dense submetric space of [Formula: see text], then the Scott rank of [Formula: see text] in the natural first-order language of metric spaces is countable and in fact at most [Formula: see text], where [Formula: see text] is the Church\u2013Kleene ordinal of [Formula: see text] (construed as a subset of [Formula: see text]) which is the least ordinal with no presentation on [Formula: see text] computable from [Formula: see text]. If [Formula: see text] is a rigid Polish metric space and [Formula: see text] is any countable dense submetric space, then the Scott rank of [Formula: see text] is countable and in fact less than [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021906132150001x","type":"journal-article","created":{"date-parts":[[2020,7,15]],"date-time":"2020-07-15T02:58:35Z","timestamp":1594781915000},"page":"2150001","source":"Crossref","is-referenced-by-count":2,"title":["Bounds on Scott ranks of some polish metric spaces"],"prefix":"10.1142","volume":"21","author":[{"given":"William","family":"Chan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Texas, Denton, TX 76203, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,7,15]]},"reference":[{"key":"S021906132150001XBIB001","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","volume":"144","author":"Ash C. 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