Groupoids, covers, and 3-uniqueness in stable theories Export

@unpublished{citeulike:5193308, abstract = {Building on Hrushovski's work in [7], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite in ternal covers. We introduce the notion of retractability of a star-definable groupoid (which is slightly stronger than Hrushovski's notion of ``eliminability''), give some criteria for when groupoids are retractable, and show how retractability relates to both 3-uniqueness and the splitness of finite internal covers. One application we give is a new direct method of constructing non-eliminable groupoids from witnesses to the failure of 3-uniqueness. Another applciation is a proof that any finite internal cover of a stable theory with a centerless liaison groupoid is almost split.}, author = {Goodrick, John and Kolesnikov, Alexei}, citeulike-article-id = {5193308}, journal = {Journal of Symbolic Logic}, keywords = {model-theory}, posted-at = {2009-07-17 16:06:38}, priority = {2}, title = {Groupoids, covers, and 3-uniqueness in stable theories}, year = {2008} }

TY - UNPB ID - citeulike:5193308 L3 - citeulike-article-id:5193308 N2 - Building on Hrushovski’s work in [7], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite in ternal covers. We introduce the notion of retractability of a star-definable groupoid (which is slightly stronger than Hrushovski’s notion of ``eliminability''), give some criteria for when groupoids are retractable, and show how retractability relates to both 3-uniqueness and the splitness of finite internal covers. One application we give is a new direct method of constructing non-eliminable groupoids from witnesses to the failure of 3-uniqueness. Another applciation is a proof that any finite internal cover of a stable theory with a centerless liaison groupoid is almost split. JF - Journal of Symbolic Logic TI - Groupoids, covers, and 3-uniqueness in stable theories KW - model-theory AU - Goodrick, John AU - Kolesnikov, Alexei PY - 2008/// ER -