## Notre Dame Journal of Formal Logic

### Stable Forking and Imaginaries

#### Abstract

We prove that a theory $T$ has stable forking if and only if $T^{\mathrm{eq}}$ has stable forking.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 4 (2018), 497-502.

Dates
Accepted: 10 May 2016
First available in Project Euclid: 17 July 2018

https://projecteuclid.org/euclid.ndjfl/1531792823

Digital Object Identifier
doi:10.1215/00294527-2018-0010

Mathematical Reviews number (MathSciNet)
MR3871898

Zentralblatt MATH identifier
06996541

Keywords
imaginaries stable forking

#### Citation

Casanovas, Enrique; Potier, Joris. Stable Forking and Imaginaries. Notre Dame J. Formal Logic 59 (2018), no. 4, 497--502. doi:10.1215/00294527-2018-0010. https://projecteuclid.org/euclid.ndjfl/1531792823

#### References

• [1] Casanovas, E., Simple Theories and Hyperimaginaries, vol. 39 of Lecture Notes in Logic, Cambridge University Press, Cambridge, 2011.
• [2] Chernikov, A., “Theories without the tree property of the second kind,” Annals of Pure and Applied Logic, vol. 165 (2014), pp. 695–723.
• [3] Kim, B., “Simplicity, and stability in there,” Journal of Symbolic Logic, vol. 66 (2001), pp. 822–36.
• [4] Kim, B., and A. Pillay, “Around stable forking,” Fundamenta Mathematicae, vol. 170 (2001), pp. 107–18.
• [5] Palacín, D., and F. O. Wagner, “Elimination of hyperimaginaries and stable independence in simple CM-trivial theories,” Notre Dame Journal of Formal Logic, vol. 54 (2013), pp. 541–51.
• [6] Peretz, A., “Geometry of forking in simple theories,” Journal of Symbolic Logic, vol. 71 (2006), pp. 347–59.
• [7] Pillay, A., Geometric Stability Theory, vol. 32 of Oxford Logic Guides, Oxford University Press, New York, 1996.
• [8] Tent, K., and M. Ziegler, A Course in Model Theory, vol. 40 of Lecture Notes in Logic, Cambridge University Press, Cambridge, 2012.