Journal of Symbolic Logic

Groupoids, covers, and 3-uniqueness in stable theories

John Goodrick and Alexei Kolesnikov

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Building on Hrushovski's work in [5], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite internal covers. We introduce the notion of retractability of a 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 application is a proof that any finite internal cover of a stable theory with a centerless liaison groupoid is almost split.

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J. Symbolic Logic, Volume 75, Issue 3 (2010), 905-929.

First available in Project Euclid: 9 July 2010

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Goodrick, John; Kolesnikov, Alexei. Groupoids, covers, and 3-uniqueness in stable theories. J. Symbolic Logic 75 (2010), no. 3, 905--929. doi:10.2178/jsl/1278682207.

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