  We show that many nice properties of a theory $T$ follow from the
corresponding properties of its reducts to finite subsignatures. If $\{ T_i
\}_{i \in I}$ is a directed family of conservative expansions of first-order
theories and each $T_i$ is stable (respectively, simple, rosy, dependent,
submodel complete, model complete, companionable), then so is the union $T :=
\cup_i T_i$. In most cases, (thorn)-forking in $T$ is equivalent to
(thorn)-forking of algebraic closures in some $T_i$.
  This applies to fields with an action by $(\mathbb{Q}, +)$, whose reducts to
finite subsignatures are interdefinable with the theory of fields with one
automorphism. We show that the model companion $\mathbb{Q}$ACFA of this theory
is strictly simple and has the same level of quantifier elimination and the
same algebraic characterization of algebraic closure and forking independence
as ACFA. The lattice of the fixed fields of the named automorphisms breaks
supersimplicity in $\mathbb{Q}$ACFA, but away from these we find many (weakly)
minimal formulas.
