$o$-stable theories

A well-developed technique created to study stable theories (M. Morley, S. Shelah) is applied in dealing with a class of theories with definable linear order. We introduce the notion of an $o$-stable theory, which generalizes the concepts of $o$-minimality, of weak $o$-minimality, and of quasi-$o$-minimality. It is proved that $o$-stable theories are dependent, but they do not exhaust the class of dependent theories with definable linear order, and that every linear order is $o$-superstable.