  We classify order $3$ linear difference operators over $\mathbb{C}(x)$ that
are solvable in terms of lower order difference operators. To prove this
result, we introduce the notion of absolute irreducibility for difference
modules, and classify modules that are irreducible but not absolutely
irreducible by using restricted and induced modules. We also show how
restriction and induction give coordinate-free formulations of sectioning and
interlacing of sequences.
