Abstract

Firstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T, canonical base of an amalgamation class $\mathscr{P}$ is the union of names of $\psi$-definitions of $\mathscr{P}, \psi$ ranging over stationary L-formulas in $\mathscr{P}$. Also, we prove that the same is true with stable formulas for an 1-based theory having elimination of hyperimaginaries. For such a theory, the stable forking property holds, too.