Abstract notions of \u201csmallness\u201d are among the most important tools that model theory offers for the analysis of arbitrary structures. The two most useful notions of this kind are forking (which is closely related to certain measure zero ideals) and thorn-forking (which generalizes the usual topological dimension). Under certain mild assumptions, forking is the finest notion of smallness, whereas thorn-forking is the coarsest.<\/p>\n\n
In this paper we study forking and thorn-forking, restricting ourselves to the class of generically stable types. Our main conclusion is that in this context these two notions coincide. We explore some applications of this equivalence.<\/p>","DOI":"10.1090\/s0002-9947-2012-05451-1","type":"journal-article","created":{"date-parts":[[2012,7,24]],"date-time":"2012-07-24T12:18:43Z","timestamp":1343132323000},"page":"1-22","source":"Crossref","is-referenced-by-count":4,"special_numbering":"932","title":["Generic stability, forking, and \u00fe-forking"],"prefix":"10.1090","volume":"365","author":[{"given":"Dar\u00edo","family":"Garc\u00eda","sequence":"first","affiliation":[]},{"given":"Alf","family":"Onshuus","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Usvyatsov","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2012,7,24]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0219061309000811","article-title":"A geometric introduction to forking and thorn-forking","volume":"9","author":"Adler, Hans","year":"2009","journal-title":"J. Math. Log.","ISSN":"http:\/\/id.crossref.org\/issn\/0219-0613","issn-type":"print"},{"key":"2","unstructured":"Dar\u00edo Garc\u00eda, Tipos gen\u00e9ricamente estables, bifurcaci\u00f3n y thorn bifurcaci\u00f3n, M. A. thesis, Universidad de los Andes, Bogot\u00e1, 2009."},{"key":"3","series-title":"Lecture Notes in Logic","isbn-type":"print","volume-title":"Stable domination and independence in algebraically closed valued fields","volume":"30","author":"Haskell, Deirdre","year":"2008","ISBN":"http:\/\/id.crossref.org\/isbn\/9780521889810"},{"issue":"4","key":"4","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.2178\/jsl\/1286198144","article-title":"Stable types in rosy theories","volume":"75","author":"Hasson, Assaf","year":"2010","journal-title":"J. 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