  We study a class of first-order theories whose complete quantifier-free types
with one free variable either have a trivial positive part or are isolated by a
positive quantifier-free formula--plus a few other technical requirements. The
theory of vector spaces and the theory fields are examples. We prove the
amalgamation property and the existence of a model-companion. We show that the
model-companion is strongly minimal. We also prove that the length of any
increasing sequence of prime types is bounded, so every formula has finite
Krull dimension.
