Translator Disclaimer
September 2010 Groupoids, covers, and 3-uniqueness in stable theories
John Goodrick, Alexei Kolesnikov
J. Symbolic Logic 75(3): 905-929 (September 2010). DOI: 10.2178/jsl/1278682207

Abstract

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.

Citation

Download Citation

John Goodrick. Alexei Kolesnikov. "Groupoids, covers, and 3-uniqueness in stable theories." J. Symbolic Logic 75 (3) 905 - 929, September 2010. https://doi.org/10.2178/jsl/1278682207

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1211.03053
MathSciNet: MR2723774
Digital Object Identifier: 10.2178/jsl/1278682207

Rights: Copyright © 2010 Association for Symbolic Logic

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.75 • No. 3 • September 2010
Back to Top