  The classical Baldwin-Lachlan characterization of uncountably categorical
theories is known to fail in continuous logic in that not every inseparably
categorical theory has a strongly minimal set. Here we investigate these issues
by developing the theory of strongly minimal sets in continuous logic and by
examining inseparably categorical expansions of Banach space.
  To this end we introduce and characterize 'dictionaric theories,' theories in
which definable sets are prevalent enough that many constructions familiar in
discrete logic can be carried out. We also introduce, in the context of Banach
theories, the notion of an 'indiscernible subspace,' which we use to improve a
result of Shelah and Usvyatsov. Both of these notions are applicable to
continuous logic outside of the context of inseparably categorical theories.
  Finally, we construct or present a slew of counterexamples, including an
$\omega$-stable theory with no Vaughtian pairs which fails to be inseparably
categorical and an inseparably categorical theory with strongly minimal sets in
its home sort only over models of sufficiently high dimension.
