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Supersimple theories
Author(s):
Steven
Buechler;
Anand
Pillay;
Frank
Wagner
Journal:
J. Amer. Math. Soc.
14
(2001),
109-124.
MSC (2000):
Primary 03C45
Posted:
September 20, 2000
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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.
References:
-
- [1]
- S. Buechler, Lascar strong types in some simple theories, Journal of Symbolic Logic, 64(1999), 817-824.
- [2]
- S. Buechler, Canonical bases in some supersimple theories, preprint 1998.
- [3]
- B. Hart and A. Pillay, A note on canonical bases, preprint 1998.
- [4]
- B. Hart, B. Kim and A. Pillay, Coordinatization and canonical bases, Journal of Symbolic Logic, 65(2000), 293-309.
- [5]
- E. Hrushovski, Pseudofinite fields and related structures, preprint 1991.
- [6]
- E. Hrushovski, Simplicity and the Lascar group, preprint 1997.
- [7]
- B. Kim, Simple first order theories, Ph.D. thesis, University of Notre Dame, 1996.
- [8]
- B. Kim, Forking in simple unstable theories, Journal of London Math. Soc., 1999. MR 2000a:03052
- [9]
- B. Kim, Recent results on simple first order theories, Proceedings Blaubeuren, London Math. Soc. Lecture Notes, Cambridge Univ. Press, 1997. MR 2000e:03100
- [10]
- B. Kim, A note on Lascar strong types in simple theories, Journal of Symbolic Logic, 63 (1998), 926-936. MR 2000a:03053
- [11]
- B. Kim, Simplicity and stability in there, to appear in Journal of Symbolic Logic.
- [12]
- B. Kim and A. Pillay, Simple theories, Annals of Pure and Applied Logic, 88 (1997). MR 99b:03049
- [13]
- D. Lascar and A. Pillay, Hyperimaginaries and automorphism groups, to appear in Journal of Symbolic Logic.
- [14]
- A. Pillay and B. Poizat, Pas d'imaginaires dans l'infini, Journal of Symbolic Logic, 52 (1987), 400-403. MR 88j:03019
- [15]
- Z. Shami, A natural finite equivalence relation definable in low theories, to appear.
- [16]
- S. Shelah, Simple unstable theories, Annals of Math. Logic, 19 (1980), 177-203. MR 82g:03055
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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:
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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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