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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Supersimple theories


Authors: Steven Buechler, Anand Pillay and Frank Wagner
Journal: J. Amer. Math. Soc. 14 (2001), 109-124
MSC (2000): Primary 03C45
Published electronically: September 20, 2000
MathSciNet review: 1800350
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Abstract:

We prove elimination of hyperimaginaries in supersimple theories. This means that if an equivalence relation on the set of realisations of a complete type (in a supersimple theory) is defined by a possibly infinite conjunction of first order formulas, then it is the intersection of definable equivalence relations.


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Additional Information

Steven Buechler
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-5683
Email: buechler.1@nd.edu

Anand Pillay
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: pillay@math.uiuc.edu

Frank Wagner
Affiliation: Mathematical Institute, Oxford University, Oxford, England
Address at time of publication: Institut Girard Desargues (Lyon I), Université Claude Bernard, 43, Boulevard du 11 Novembre 1918, 69622 Villeurbanne-Cedex, France
Email: wagner@desargues.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-00-00350-7
PII: S 0894-0347(00)00350-7
Received by editor(s): July 14, 1999
Received by editor(s) in revised form: June 20, 2000
Published electronically: September 20, 2000
Additional Notes: The first author was supported by an NSF grant. The second author was supported by an NSF grant and thanks MSRI for its hospitality. The third author was supported by DFG grant Wa 899/2-1 and thanks MSRI for its hospitality.
Article copyright: © Copyright 2000 American Mathematical Society