{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:25Z","timestamp":1753880845301,"version":"3.41.2"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"FWF","award":["P28153","P29999"],"award-info":[{"award-number":["P28153","P29999"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p> We generalize the [Formula: see text] dichotomy to doubly-indexed sequences of analytic digraphs. Under a mild definability assumption, we use this generalization to characterize the family of Borel actions of tsi Polish groups on Polish spaces that can be decomposed into countably-many Borel actions admitting complete Borel sets that are lacunary with respect to an open neighborhood of the identity. We also show that if the group in question is non-archimedean, then the inexistence of such a decomposition yields a special kind of continuous embedding of [Formula: see text] into the corresponding orbit equivalence relation. <\/jats:p>","DOI":"10.1142\/s0219061321500288","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T10:40:41Z","timestamp":1622457641000},"source":"Crossref","is-referenced-by-count":0,"title":["A generalization of the \ud835\udd3e0 dichotomy and a strengthening of the \ud835\udd3c0\u2115 dichotomy"],"prefix":"10.1142","volume":"22","author":[{"given":"Benjamin D.","family":"Miller","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Vienna, Oskar Morgenstern Platz 1, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"S0219061321500288BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0219061321500288BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1998.1771"},{"key":"S0219061321500288BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1952-0047250-4"},{"key":"S0219061321500288BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-98-00258-6"},{"key":"S0219061321500288BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735264"},{"key":"S0219061321500288BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2013.10.034"},{"key":"S0219061321500288BIB007","doi-asserted-by":"publisher","DOI":"10.4064\/fm170-1-2"},{"key":"S0219061321500288BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/14982"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061321500288","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T04:07:04Z","timestamp":1665374824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061321500288"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,5]]},"references-count":8,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["10.1142\/S0219061321500288"],"URL":"https:\/\/doi.org\/10.1142\/s0219061321500288","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2021,7,5]]},"article-number":"2150028"}}