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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-6,
author = {Byunghan Kim and A. Pillay},
title = {Around stable forking},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {107-118},
zbl = {0987.03034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-6}
}
Byunghan Kim; A. Pillay. Around stable forking. Fundamenta Mathematicae, Tome 167 (2001) pp. 107-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-6/