{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T12:33:35Z","timestamp":1764333215772,"version":"3.41.2"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> The aim of this paper is to generalize and improve two of the main model-theoretic results of \u201cStable group theory and approximate subgroups\u201d by Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence of Lie models. The second one is the Stabilizer Theorem. In the process, a systematic study of the structure of piecewise hyperdefinable sets is developed. In particular, we show the most significant properties of their logic topologies. <\/jats:p>","DOI":"10.1142\/s0219061322500271","type":"journal-article","created":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T14:36:16Z","timestamp":1671201376000},"source":"Crossref","is-referenced-by-count":3,"title":["On piecewise hyperdefinable groups"],"prefix":"10.1142","volume":"23","author":[{"given":"A. Rodriguez","family":"Fanlo","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK"},{"name":"Current address: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel"}]}],"member":"219","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"issue":"3","key":"S0219061322500271BIB002","doi-asserted-by":"crossref","first-page":"829","DOI":"10.2178\/jsl\/1122038916","volume":"70","author":"Ben-Yaacov I.","year":"2005","journal-title":"J. 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