Geometry of forking in simple theories

  title={Geometry of forking in simple theories},
  author={Assaf Peretz},
  journal={Journal of Symbolic Logic},
  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. 

Topics from this paper

We give two alternative proofs that 1-based theories of finite SU-rank have stable forking, neither of which seems to require the full power of elimination of hyperimaginaries. We also show someExpand
Stable Forking and Imaginaries
We prove that a theory $T$ has stable forking if and only if $T^\mathrm{eq}$ has stable forking.
Omega-categorical simple theories
This thesis touches on many different aspects of homogeneous relational structures. We start with an introductory chapter in which we present all the background from model theory and homogeneityExpand
On Weak Elimination of Hyperimaginaries and its Consequences
We analyze the notion of weak elimination of hyperimaginaries (WEHI) in simple theories. A key observation in the analysis is a characterization of WEHI in terms of forking dependence -- a conditionExpand
What Simplicity Is Not
Hilbert’s 24th problem, and a mathematical concept of simplicity of a proof, are investigated, with both sides focused on what simplicity is not. Expand
Forking in simple theories and CM-triviality
Aquesta tesi te tres objectius. En primer lloc, estudiem generalitzacions de la jerarquia no ample relatives a una familia de tipus parcials. Aquestes jerarquies en permeten classificar laExpand


Simplicity, and stability in there
  • Byunghan Kim
  • Computer Science, Mathematics
  • Journal of Symbolic Logic
  • 2001
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
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