{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:26:44Z","timestamp":1775053604659,"version":"3.50.1"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":284,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a commentary on Newelski's suggestion or conjecture [8] that topological dynamics, in the sense of Ellis [3], applied to the action of a definable group<jats:italic>G<\/jats:italic>(<jats:italic>M<\/jats:italic>) on its \u201cexternal type space\u201d<jats:italic>S<jats:sub>G.ext<\/jats:sub><\/jats:italic>(<jats:italic>M<\/jats:italic>), can explain, account for, or give rise to, the quotient<jats:italic>G<\/jats:italic>\/<jats:italic>G<\/jats:italic><jats:sup>00<\/jats:sup>, at least for suitable groups in<jats:italic>NIP<\/jats:italic>theories. We give a positive answer for measure-stable (or<jats:italic>f sg<\/jats:italic>) groups in<jats:italic>NIP<\/jats:italic>theories. As part of our analysis we show the existence of \u201cexternally definable\u201d generics of<jats:italic>G<\/jats:italic>(<jats:italic>M<\/jats:italic>) for measure-stable groups. We also point out that for<jats:italic>G<\/jats:italic>definably amenable (in a<jats:italic>NIP<\/jats:italic>theory)<jats:italic>G<\/jats:italic>\/<jats:italic>G<\/jats:italic><jats:sup>00<\/jats:sup>can be recovered, via the Ellis theory, from a natural Ellis semigroup structure on the space of global<jats:italic>f<\/jats:italic>-generic types.<\/jats:p>","DOI":"10.2178\/jsl.7802170","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T14:11:08Z","timestamp":1368627068000},"page":"657-666","source":"Crossref","is-referenced-by-count":11,"title":["Topological dynamics and definable groups"],"prefix":"10.1017","volume":"78","author":[{"given":"Anand","family":"Pillay","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000190_ref011","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061304000346"},{"key":"S0022481200000190_ref010","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534372.001.0001","volume-title":"Geometric stability theory","author":"Pillay","year":"1996"},{"key":"S0022481200000190_ref008","first-page":"50","volume":"74","author":"Newelski","year":"2009","journal-title":"Topological dynamics of definable group actions"},{"key":"S0022481200000190_ref006","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-1814705"},{"key":"S0022481200000190_ref005","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/274"},{"key":"S0022481200000190_ref003","volume-title":"Lectures on topological dynamics","author":"Ellis","year":"1969"},{"key":"S0022481200000190_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-07-00558-9"},{"key":"S0022481200000190_ref002","first-page":"1","volume":"77","author":"Chernikov","year":"2012","journal-title":"Forking and dividing in NTP2 theories"},{"key":"S0022481200000190_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2012-05626-1"},{"key":"S0022481200000190_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0202-6"},{"key":"S0022481200000190_ref001","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0913","volume-title":"The topological dynamics of Ellis actions","author":"Akin","year":"2008"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T19:09:50Z","timestamp":1715368190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000190\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["S0022481200000190"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7802170","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}