{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:02:20Z","timestamp":1759147340319},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1197,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of <jats:italic>m<\/jats:italic>-independent extensions (we call them compact <jats:italic>e<\/jats:italic>-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of <jats:italic>m<\/jats:italic>-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact <jats:italic>e<\/jats:italic>-structures. In particular, we notice that a variant of the group configuration theorem holds in this context.<\/jats:p><jats:p>A general construction of compact structures is described. Using it, a class of examples of compact <jats:italic>e<\/jats:italic>-structures which are not small is constructed.<\/jats:p><jats:p>It is also noticed that in an <jats:italic>m<\/jats:italic>-stable compact <jats:italic>e<\/jats:italic>-structure every orbit is equidominant with a product of <jats:italic>m<\/jats:italic>-regular orbits.<\/jats:p>","DOI":"10.2178\/jsl\/1286198141","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T09:16:13Z","timestamp":1286183773000},"page":"1147-1175","source":"Crossref","is-referenced-by-count":2,"title":["Generalizations of small profinite structures"],"prefix":"10.1017","volume":"75","author":[{"given":"Krzysztof","family":"Krupi\u0144ski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002188_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.10.007"},{"key":"S0022481200002188_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm185-1-3"},{"key":"S0022481200002188_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.01.011"},{"key":"S0022481200002188_ref008","first-page":"127","volume":"66","author":"Lascar","year":"2001","journal-title":"Hyperimaginaries and automorphism groups"},{"key":"S0022481200002188_ref011","first-page":"1375","volume":"64","author":"Newelski","year":"1999","journal-title":"Geometry of *-finite types"},{"key":"S0022481200002188_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-01-02854-9"},{"key":"S0022481200002188_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3002-0"},{"key":"S0022481200002188_ref012","doi-asserted-by":"publisher","DOI":"10.4064\/fm170-1-9"},{"key":"S0022481200002188_ref013","first-page":"859","volume":"66","author":"Newelski","year":"2001","journal-title":"Small profinite groups"},{"key":"S0022481200002188_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02773473"},{"key":"S0022481200002188_ref010","first-page":"1261","volume":"64","author":"Newelski","year":"1999","journal-title":"Flat Morley sequences"},{"key":"S0022481200002188_ref001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061301000119"},{"key":"S0022481200002188_ref002","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.jalgebra.2006.01.027","article-title":"Small profinite groups and rings","volume":"306","author":"Wagner","year":"2006","journal-title":"Journal of Algebra"},{"key":"S0022481200002188_ref016","doi-asserted-by":"publisher","DOI":"10.4064\/fm176-2-6"},{"key":"S0022481200002188_ref007","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1305\/ndjfl\/1074396308","article-title":"On bounded type-definable equivalence relations","volume":"43","author":"Krupi\u0144ski","year":"2002","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200002188_ref003","first-page":"926","volume":"63","author":"Kim","year":"2000","journal-title":"A note on Lascar strong types in simple theories"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002188","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T16:36:50Z","timestamp":1556383010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002188\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0022481200002188"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1286198141","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}