  Let $G$ be a group with undecidable domino problem (such as $\mathbb{Z}^2$).
We prove the undecidability of all nontrivial dynamical properties for sofic
$G$-subshifts, that such a result fails for SFTs, and an undecidability result
for dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem. For
$G$ amenable we prove that topological entropy is not computable from
presentations of SFTs, and a more general result for dynamical invariants
taking values in partially ordered sets.
