Geometry of forking in simple theories

@article{Peretz2006GeometryOF,
  title={Geometry of forking in simple theories},
  author={Assaf Peretz},
  journal={Journal of Symbolic Logic},
  year={2006},
  volume={71},
  pages={347 - 360}
}
  • Assaf Peretz
  • Published 2006
  • Mathematics, Computer Science
  • Journal of Symbolic Logic
Abstract We investigate the geometry of forking for SU-rank 2 elements in supersimple ω-categorical theories and prove stable forking and some structural properties for such elements. We extend this analysis to the case of SU-rank 3 elements. 

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References

SHOWING 1-7 OF 7 REFERENCES
Simplicity, and stability in there
  • Byunghan Kim
  • Computer Science, Mathematics
  • Journal of Symbolic Logic
  • 2001
TLDR
It is proved that the equivalence of simplicity and the symmetry of forking is equal, and the same is true with stable formulas for an 1-based theory having elimination of hyperimaginaries. Expand
Simple unstable theories
Abstract We point out a class of unstable theories which are simple, and develop for them an analog to the basic theorems on stable theories.
Simple Theories
TLDR
This paper succeeds in proving the Independence Theorem over a model for simple theories by proving that any theory equipped with a notion of independence satisfying all the basic algebraic axioms must be simple, and that moreover the notion ofindependence must coincide with nonforking. Expand
Around stable forking
In the past few years various conjectures have been made concerning therelationship between simple theories and stable theories. The general thrustis that in a simple theory T forking should beExpand
Classification theory
  • North-Holland, Amsterdam
  • 1978
Investigations into the geometry of forking in simple theories
  • Ph.D. thesis, UC Berekeley
  • 2003
Simplicity