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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Supersimple theories
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by Steven Buechler, Anand Pillay and Frank Wagner PDF
J. Amer. Math. Soc. 14 (2001), 109-124 Request permission


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:
  • Anand Pillay
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
  • MR Author ID: 139610
  • Email:
  • 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:
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 109-124
  • MSC (2000): Primary 03C45
  • DOI:
  • MathSciNet review: 1800350