The Lascar group and the strong types of hyperimaginaries. (English) Zbl 1286.03124

Summary: This is an expository note on the Lascar group. We also study the Lascar group over hyperimaginaries and make some new observations on the strong types over those. In particular, we show that in a simple theory \(\operatorname{Ltp}\equiv\operatorname{stp}\) in real context implies that for hyperimaginary context.


03C45 Classification theory, stability, and related concepts in model theory
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[1] Casanovas, E., D. Lascar, A. Pillay, and M. Ziegler, “Galois groups of first order theories,” Journal of Mathematical Logic , vol. 1(2001), pp. 305-19. · Zbl 0993.03048
[2] Casanovas, E., and J. Potier “Normal hyperimaginaries,” preprint, [math.LO]. · Zbl 1328.03034
[3] Gismatullin, J., and L. Newelski, “\(G\)-compactness and groups,” Archive for Mathematical Logic , vol. 47 (2008), pp. 479-501. · Zbl 1146.03018
[4] Goodrick, J., B. Kim, and A. Kolesnikov, “Homology groups of types in model theory and the computation of \(H_{2}(p)\),” to appear in Journal of Symbolic Logic . · Zbl 1349.03031
[5] Goodrick, J., B. Kim, and A. Kolesnikov, “Amalgamation functors and homology groups in model theory,” preprint, 2013. · Zbl 1303.03071
[6] Hrushovski, E., “Simplicity and the Lascar group,” unpublished note, 1998.
[7] Kim, B., “A note on Lascar strong types in simple theories” Journal of Symbolic Logic , vol. 63 (1998), pp. 926-36. · Zbl 0961.03030
[8] Lascar, D., “On the category of models of a complete theory,” Journal of Symbolic Logic , vol. 47 (1982), pp. 249-66. · Zbl 0498.03019
[9] Lascar, D., and A. Pillay, “Hyperimaginaries and automorphism groups,” Journal of Symbolic Logic , vol. 66 (2001), pp. 127-43. · Zbl 1002.03027
[10] Wagner, F. O., Simple Theories , vol. 503 of Mathematics and its Applications , Kluwer, Dordrecht, 2000. · Zbl 0948.03032
[11] Ziegler, M., “Introduction to the Lascar group,” pp. 279-98 in Tits buildings and the model theory of groups (Würzburg, 2000) , vol. 291 of London Mathematical Society Lecture Note Series , Cambridge University Press, Cambridge, 2002.
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