{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:15:45Z","timestamp":1753884945157,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100003074","name":"Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica de Argentina","doi-asserted-by":"crossref","award":["PICT 2018-2315"],"award-info":[{"award-number":["PICT 2018-2315"]}],"id":[{"id":"10.13039\/501100003074","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NSF","award":["DMS-1800323"],"award-info":[{"award-number":["DMS-1800323"]}]},{"name":"The National Science Centre of Poland, NCN","award":["2019\/34\/E\/ST1\/00082"],"award-info":[{"award-number":["2019\/34\/E\/ST1\/00082"]}]},{"name":"the National Science Centre, Poland, NCN","award":["2019\/35\/O\/ST1\/02266"],"award-info":[{"award-number":["2019\/35\/O\/ST1\/02266"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base b is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between [Formula: see text] sets. We also show that the effective versions of these results hold in the effective Borel hierarchy. <\/jats:p>","DOI":"10.1142\/s0219061324500193","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T09:08:28Z","timestamp":1710493708000},"source":"Crossref","is-referenced-by-count":0,"title":["The descriptive complexity of the set of Poisson generic numbers"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5425-8563","authenticated-orcid":false,"given":"Ver\u00f3nica","family":"Becher","sequence":"first","affiliation":[{"name":"Departamento de Computaci\u00f3n, Facultad de Ciencias Exactas y Naturales & ICC, Universidad de Buenos Aires & CONICET, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2399-0129","authenticated-orcid":false,"given":"Stephen","family":"Jackson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of North Texas, General Academics Building 435, 1155 Union Circle, #311430, Denton, TX 76203-5017, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7794-2835","authenticated-orcid":false,"given":"Dominik","family":"Kwietniak","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Jagiellonian University in Krak\u00f3w, ul. \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8379-9484","authenticated-orcid":false,"given":"Bill","family":"Mance","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"S0219061324500193BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/8001"},{"issue":"1","key":"S0219061324500193BIB002","first-page":"170","volume":"74","author":"Airey D.","year":"2022","journal-title":"J. Symb. Log."},{"key":"S0219061324500193BIB003","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnac234"},{"key":"S0219061324500193BIB004","doi-asserted-by":"publisher","DOI":"10.4064\/fm226-1-4"},{"key":"S0219061324500193BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3806"},{"key":"S0219061324500193BIB006","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdu035"},{"key":"S0219061324500193BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.02.022"},{"key":"S0219061324500193BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0219061324500193BIB010","doi-asserted-by":"publisher","DOI":"10.4064\/fm-144-2-163-179"},{"volume-title":"Jean-Morlet Chair Conf. Diophantine Problems, Determinism and Randomness","series-title":"Centre International de Rencontres Math\u00e9matiques","author":"Weiss B.","key":"S0219061324500193BIB011"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061324500193","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T07:06:11Z","timestamp":1744268771000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061324500193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,9]]},"references-count":10,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["10.1142\/S0219061324500193"],"URL":"https:\/\/doi.org\/10.1142\/s0219061324500193","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2024,5,9]]},"article-number":"2450019"}}