Around stable forking
Volume 170 / 2001
Fundamenta Mathematicae 170 (2001), 107-118 MSC: Primary 03C45. DOI: 10.4064/fm170-1-6
We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory $T$ has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.