{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T21:53:46Z","timestamp":1726005226197},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> We develop \u201clocal NIP group theory\u201d in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure [Formula: see text] expanding a group, and left invariant NIP formula [Formula: see text], we prove various aspects of \u201clocal fsg\u201d for the right-stratified formula [Formula: see text]. This includes a [Formula: see text]-type-definable connected component, uniqueness of the pseudofinite counting measure as a left-invariant measure on [Formula: see text]-formulas and generic compact domination for [Formula: see text]-definable sets. <\/jats:p>","DOI":"10.1142\/s0219061321500094","type":"journal-article","created":{"date-parts":[[2020,9,8]],"date-time":"2020-09-08T15:16:15Z","timestamp":1599578175000},"page":"2150009","source":"Crossref","is-referenced-by-count":2,"title":["Pseudofinite groups and VC-dimension"],"prefix":"10.1142","volume":"21","author":[{"given":"Gabriel","family":"Conant","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, UK"}]},{"given":"Anand","family":"Pillay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46656, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"key":"S0219061321500094BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/jams\/896"},{"key":"S0219061321500094BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004118000798"},{"key":"S0219061321500094BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-005-0509-8"},{"key":"S0219061321500094BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187876"},{"key":"S0219061321500094BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-07-00558-9"},{"key":"S0219061321500094BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758643"},{"key":"S0219061321500094BIB008","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/274"},{"key":"S0219061321500094BIB009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2012-05626-1"},{"key":"S0219061321500094BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187833"},{"key":"S0219061321500094BIB011","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1074396308"},{"key":"S0219061321500094BIB012","doi-asserted-by":"publisher","DOI":"10.2307\/2694914"},{"key":"S0219061321500094BIB013","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1231082302"},{"key":"S0219061321500094BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061304000346"},{"key":"S0219061321500094BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8622-1"},{"key":"S0219061321500094BIB016","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107415133"},{"key":"S0219061321500094BIB017","doi-asserted-by":"publisher","DOI":"10.4064\/fm231-1-5"},{"key":"S0219061321500094BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1457-3"},{"key":"S0219061321500094BIB019","doi-asserted-by":"publisher","DOI":"10.1112\/blms.12211"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061321500094","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T09:09:05Z","timestamp":1627290545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061321500094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,2]]},"references-count":18,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S0219061321500094"],"URL":"https:\/\/doi.org\/10.1142\/s0219061321500094","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,2]]}}}