  Distorted sums of models were introduced and discussed in [Sh:463]. This
notion generalizes the notion of disjoint (or direct) sums of models by letting
the summands overlap. In the first section we investigate types in distorted
sums and show that the type of a sequence of elements A is determined by the
`local' type of A (i.e. the type restricted to a neighborhood of A). We
simplify the proofs in [Sh:463] and improve the bounds on the radii needed to
determine the types.
  Natural examples of distorted sums are models with distant functions. In the
second and third sections we discuss such models and improve a theorem by
Gaifman, that states that each formula is equivalent to a boolean combination
of local formulas.
