We show that the class of groups where EDT0L languages can be used to describe solution sets systems equations is closed under direct products, wreath products with finite groups, and passing index subgroups. also add contain a product hyperbolic as subgroup list solutions expressed an language. This includes dihedral Artin groups. rational constraints in virtually abelian have solutions, addit...

We prove that every dynamical system $X$ with a free action of countable amenable group $G$ by homeomorphisms has zero-dimensional extension $Y$ which is faithful and principal, i.e. $G$-invariant measure $\mu $ on exactly one preimage