We study the notion of weak dividing introduced by S. Shelah. In particular we prove that T is stable iff weak dividing is symmetric. In order to study simple theories Shelah originally defined weak dividing in [6] . This notion is overshadowed by that of dividing, as the first author proved that dividing is the right well-behaved notion for simple theories [2],[3],[5],and [4]. However Dolich’s...

The aim of this paper is to define various properties of formulas in first order theories, and prove the appropriate implications between these properties. Most definitions are taken from [3], but the definitions themselves and many of the proofs are due to Shelah (see [4, II]). We give citations at the beginning of proofs taken from other sources. Recall that a theory is stable if no formula h...