  We give several new characterizations of $IP$ (the independence property) and
$SOP$ (the strict order property) for continuous first order logic and study
their relations to the function theory and the Banach space theory. We suggest
new dividing lines of unstable theories by the study of subclasses of Baire-1
functions and argue why one should not expect a perfect analog of Shelah's
theorem, namely a theory is unstable iff it has $IP$ or $SOP$, for real-valued
logics, especially for continuous logic.
