  We extend Yves Andr\'e's theory of solution algebras in differential Galois
theory to a general Tannakian context. As applications, we establish analogues
of his correspondence between solution fields and observable subgroups of the
Galois group for iterated differential equations in positive characteristic and
for difference equations. The use of solution algebras in the difference
algebraic context also allows a new approach to recent results of Philippon and
Adamczewski--Faverjon in transcendence theory.
