{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T06:19:11Z","timestamp":1775715551035,"version":"3.50.1"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1349399"],"award-info":[{"award-number":["1349399"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We show that the following operator algebras have hyperarithmetic theory: the hyperfinite II$_1$ factor $\\mathcal R$, $L(\\varGamma )$ for $\\varGamma $ a finitely generated group with solvable word problem, $C^*(\\varGamma )$ for $\\varGamma $ a finitely presented group, $C^*_\\lambda (\\varGamma )$ for $\\varGamma $ a finitely generated group with solvable word problem, $C(2^\\omega )$ and $C(\\mathbb P)$ (where $\\mathbb P$ is the pseudoarc). We also show that the Cuntz algebra $\\mathcal O_2$ has a hyperarithmetic theory provided that the Kirchberg embedding problems have affirmative answers. Finally, we prove that if there is an existentially closed (e.c.) II$_1$ factor (resp. $\\textrm{C}^*$-algebra) that does not have hyperarithmetic theory, then there are continuum many theories of e.c. II$_1$ factors (resp. e.c. $\\textrm{C}^*$-algebras).<\/jats:p>","DOI":"10.1093\/logcom\/exaa059","type":"journal-article","created":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T11:13:34Z","timestamp":1599390814000},"page":"612-629","source":"Crossref","is-referenced-by-count":5,"title":["Operator algebras with hyperarithmetic theory"],"prefix":"10.1093","volume":"31","author":[{"given":"Isaac","family":"Goldbring","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California, Irvine, 340 Rowland Hall (Bldg.# 400), Irvine, CA 92697, USA"}]},{"given":"Bradd","family":"Hart","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, 1280 Main St., Hamilton, Ontario L8S 4L8, Canada"}]}],"member":"286","published-online":{"date-parts":[[2020,9,23]]},"reference":[{"key":"2021030623535832300_ref1","author":"Barwise","journal-title":"Admissible Sets and 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